Finite Math Examples

$(2 x - y) - 12 i = 16 + 6 y i$

Step 1

Solve the equation for $y$ .

Tap for more steps...

Step 1.1

Subtract $6 y i$ from both sides of the equation.

$2 x - y - 12 i - 6 y i = 16$

Step 1.2

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 1.2.1

Subtract $2 x$ from both sides of the equation.

$- y - 12 i - 6 y i = 16 - 2 x$

Step 1.2.2

Add $12 i$ to both sides of the equation.

$- y - 6 y i = 16 - 2 x + 12 i$

Step 1.3

Factor $y$ out of $- y - 6 y i$ .

Tap for more steps...

Step 1.3.1

Factor $y$ out of $- y$ .

$y \cdot - 1 - 6 y i = 16 - 2 x + 12 i$

Step 1.3.2

Factor $y$ out of $- 6 y i$ .

$y \cdot - 1 + y (- 6 i) = 16 - 2 x + 12 i$

Step 1.3.3

Factor $y$ out of $y \cdot - 1 + y (- 6 i)$ .

$y (- 1 - 6 i) = 16 - 2 x + 12 i$

Step 1.4

Divide each term in $y (- 1 - 6 i) = 16 - 2 x + 12 i$ by $- 1 - 6 i$ and simplify.

Tap for more steps...

Step 1.4.1

Divide each term in $y (- 1 - 6 i) = 16 - 2 x + 12 i$ by $- 1 - 6 i$ .

$\frac{y (- 1 - 6 i)}{- 1 - 6 i} = \frac{16}{- 1 - 6 i} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.2

Simplify the left side.

Tap for more steps...

Step 1.4.2.1

Cancel the common factor of $- 1 - 6 i$ .

Tap for more steps...

Step 1.4.2.1.1

Cancel the common factor.

$\frac{y (- 1 - 6 i)}{- 1 - 6 i} = \frac{16}{- 1 - 6 i} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{16}{- 1 - 6 i} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3

Simplify the right side.

Tap for more steps...

Step 1.4.3.1

Simplify terms.

Tap for more steps...

Step 1.4.3.1.1

Simplify each term.

Tap for more steps...

Step 1.4.3.1.1.1

Multiply the numerator and denominator of $\frac{16}{- 1 - 6 i}$ by the conjugate of $- 1 - 6 i$ to make the denominator real.

$y = \frac{16}{- 1 - 6 i} \cdot \frac{- 1 + 6 i}{- 1 + 6 i} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2

Multiply.

Tap for more steps...

Step 1.4.3.1.1.2.1

Combine.

$y = \frac{16 (- 1 + 6 i)}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.2

Simplify the numerator.

Tap for more steps...

Step 1.4.3.1.1.2.2.1

Apply the distributive property.

$y = \frac{16 \cdot - 1 + 16 (6 i)}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.2.2

Multiply $16$ by $- 1$ .

$y = \frac{- 16 + 16 (6 i)}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.2.3

Multiply $6$ by $16$ .

$y = \frac{- 16 + 96 i}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3

Simplify the denominator.

Tap for more steps...

Step 1.4.3.1.1.2.3.1

Expand $(- 1 - 6 i) (- 1 + 6 i)$ using the FOIL Method.

Tap for more steps...

Step 1.4.3.1.1.2.3.1.1

Apply the distributive property.

$y = \frac{- 16 + 96 i}{- 1 (- 1 + 6 i) - 6 i (- 1 + 6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.1.2

Apply the distributive property.

$y = \frac{- 16 + 96 i}{- 1 \cdot - 1 - 1 (6 i) - 6 i (- 1 + 6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.1.3

Apply the distributive property.

$y = \frac{- 16 + 96 i}{- 1 \cdot - 1 - 1 (6 i) - 6 i \cdot - 1 - 6 i (6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2

Simplify.

Tap for more steps...

Step 1.4.3.1.1.2.3.2.1

Multiply $- 1$ by $- 1$ .

$y = \frac{- 16 + 96 i}{1 - 1 (6 i) - 6 i \cdot - 1 - 6 i (6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.2

Multiply $6$ by $- 1$ .

$y = \frac{- 16 + 96 i}{1 - 6 i - 6 i \cdot - 1 - 6 i (6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.3

Multiply $- 1$ by $- 6$ .

$y = \frac{- 16 + 96 i}{1 - 6 i + 6 i - 6 i (6 i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.4

Multiply $6$ by $- 6$ .

$y = \frac{- 16 + 96 i}{1 - 6 i + 6 i - 36 i i} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.5

Raise $i$ to the power of $1$ .

$y = \frac{- 16 + 96 i}{1 - 6 i + 6 i - 36 (i^{1} i)} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.6

Raise $i$ to the power of $1$ .

$y = \frac{- 16 + 96 i}{1 - 6 i + 6 i - 36 (i^{1} i^{1})} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{- 16 + 96 i}{1 - 6 i + 6 i - 36 i^{1 + 1}} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.8

Add $1$ and $1$ .

$y = \frac{- 16 + 96 i}{1 - 6 i + 6 i - 36 i^{2}} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.9

Add $- 6 i$ and $6 i$ .

$y = \frac{- 16 + 96 i}{1 + 0 - 36 i^{2}} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.2.10

Add $1$ and $0$ .

$y = \frac{- 16 + 96 i}{1 - 36 i^{2}} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.3

Simplify each term.

Tap for more steps...

Step 1.4.3.1.1.2.3.3.1

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{- 16 + 96 i}{1 - 36 \cdot - 1} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.3.2

Multiply $- 36$ by $- 1$ .

$y = \frac{- 16 + 96 i}{1 + 36} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.2.3.4

Add $1$ and $36$ .

$y = \frac{- 16 + 96 i}{37} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.3

Split the fraction $\frac{- 16 + 96 i}{37}$ into two fractions.

$y = \frac{- 16}{37} + \frac{96 i}{37} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.4

Move the negative in front of the fraction.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{- 2 x}{- 1 - 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.5

Multiply the numerator and denominator of $\frac{- 2 x}{- 1 - 6 i}$ by the conjugate of $- 1 - 6 i$ to make the denominator real.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{- 2 x}{- 1 - 6 i} \cdot \frac{- 1 + 6 i}{- 1 + 6 i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6

Multiply.

Tap for more steps...

Step 1.4.3.1.1.6.1

Combine.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{- 2 x (- 1 + 6 i)}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.2

Simplify the numerator.

Tap for more steps...

Step 1.4.3.1.1.6.2.1

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{- 2 x \cdot - 1 - 2 x (6 i)}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.2.2

Multiply $- 1$ by $- 2$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 2 x (6 i)}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.2.3

Multiply $6$ by $- 2$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{(- 1 - 6 i) (- 1 + 6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3

Simplify the denominator.

Tap for more steps...

Step 1.4.3.1.1.6.3.1

Expand $(- 1 - 6 i) (- 1 + 6 i)$ using the FOIL Method.

Tap for more steps...

Step 1.4.3.1.1.6.3.1.1

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{- 1 (- 1 + 6 i) - 6 i (- 1 + 6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.1.2

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{- 1 \cdot - 1 - 1 (6 i) - 6 i (- 1 + 6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.1.3

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{- 1 \cdot - 1 - 1 (6 i) - 6 i \cdot - 1 - 6 i (6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2

Simplify.

Tap for more steps...

Step 1.4.3.1.1.6.3.2.1

Multiply $- 1$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 1 (6 i) - 6 i \cdot - 1 - 6 i (6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.2

Multiply $6$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i - 6 i \cdot - 1 - 6 i (6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.3

Multiply $- 1$ by $- 6$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i + 6 i - 6 i (6 i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.4

Multiply $6$ by $- 6$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i + 6 i - 36 i i} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.5

Raise $i$ to the power of $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i + 6 i - 36 (i^{1} i)} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.6

Raise $i$ to the power of $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i + 6 i - 36 (i^{1} i^{1})} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i + 6 i - 36 i^{1 + 1}} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.8

Add $1$ and $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 6 i + 6 i - 36 i^{2}} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.9

Add $- 6 i$ and $6 i$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 + 0 - 36 i^{2}} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.2.10

Add $1$ and $0$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 36 i^{2}} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.3

Simplify each term.

Tap for more steps...

Step 1.4.3.1.1.6.3.3.1

Rewrite $i^{2}$ as $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 - 36 \cdot - 1} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.3.2

Multiply $- 36$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{1 + 36} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.6.3.4

Add $1$ and $36$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x - 12 x i}{37} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.7

Factor $2 x$ out of $2 x - 12 x i$ .

Tap for more steps...

Step 1.4.3.1.1.7.1

Factor $2 x$ out of $2 x$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1) - 12 x i}{37} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.7.2

Factor $2 x$ out of $- 12 x i$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1) + 2 x (- 6 i)}{37} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.7.3

Factor $2 x$ out of $2 x (1) + 2 x (- 6 i)$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{12 i}{- 1 - 6 i}$

Step 1.4.3.1.1.8

Multiply the numerator and denominator of $\frac{12 i}{- 1 - 6 i}$ by the conjugate of $- 1 - 6 i$ to make the denominator real.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{12 i}{- 1 - 6 i} \cdot \frac{- 1 + 6 i}{- 1 + 6 i}$

Step 1.4.3.1.1.9

Multiply.

Tap for more steps...

Step 1.4.3.1.1.9.1

Combine.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{12 i (- 1 + 6 i)}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2

Simplify the numerator.

Tap for more steps...

Step 1.4.3.1.1.9.2.1

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{12 i \cdot - 1 + 12 i (6 i)}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.2

Multiply $- 1$ by $12$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 12 i (6 i)}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.3

Multiply $12 i (6 i)$ .

Tap for more steps...

Step 1.4.3.1.1.9.2.3.1

Multiply $6$ by $12$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 72 i i}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.3.2

Raise $i$ to the power of $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 72 (i^{1} i)}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.3.3

Raise $i$ to the power of $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 72 (i^{1} i^{1})}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 72 i^{1 + 1}}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.3.5

Add $1$ and $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 72 i^{2}}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.4

Simplify each term.

Tap for more steps...

Step 1.4.3.1.1.9.2.4.1

Rewrite $i^{2}$ as $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i + 72 \cdot - 1}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.4.2

Multiply $72$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 12 i - 72}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.2.5

Reorder $- 12 i$ and $- 72$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{(- 1 - 6 i) (- 1 + 6 i)}$

Step 1.4.3.1.1.9.3

Simplify the denominator.

Tap for more steps...

Step 1.4.3.1.1.9.3.1

Expand $(- 1 - 6 i) (- 1 + 6 i)$ using the FOIL Method.

Tap for more steps...

Step 1.4.3.1.1.9.3.1.1

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{- 1 (- 1 + 6 i) - 6 i (- 1 + 6 i)}$

Step 1.4.3.1.1.9.3.1.2

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{- 1 \cdot - 1 - 1 (6 i) - 6 i (- 1 + 6 i)}$

Step 1.4.3.1.1.9.3.1.3

Apply the distributive property.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{- 1 \cdot - 1 - 1 (6 i) - 6 i \cdot - 1 - 6 i (6 i)}$

Step 1.4.3.1.1.9.3.2

Simplify.

Tap for more steps...

Step 1.4.3.1.1.9.3.2.1

Multiply $- 1$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 1 (6 i) - 6 i \cdot - 1 - 6 i (6 i)}$

Step 1.4.3.1.1.9.3.2.2

Multiply $6$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i - 6 i \cdot - 1 - 6 i (6 i)}$

Step 1.4.3.1.1.9.3.2.3

Multiply $- 1$ by $- 6$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i + 6 i - 6 i (6 i)}$

Step 1.4.3.1.1.9.3.2.4

Multiply $6$ by $- 6$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i + 6 i - 36 i i}$

Step 1.4.3.1.1.9.3.2.5

Raise $i$ to the power of $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i + 6 i - 36 (i^{1} i)}$

Step 1.4.3.1.1.9.3.2.6

Raise $i$ to the power of $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i + 6 i - 36 (i^{1} i^{1})}$

Step 1.4.3.1.1.9.3.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i + 6 i - 36 i^{1 + 1}}$

Step 1.4.3.1.1.9.3.2.8

Add $1$ and $1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 6 i + 6 i - 36 i^{2}}$

Step 1.4.3.1.1.9.3.2.9

Add $- 6 i$ and $6 i$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 + 0 - 36 i^{2}}$

Step 1.4.3.1.1.9.3.2.10

Add $1$ and $0$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 36 i^{2}}$

Step 1.4.3.1.1.9.3.3

Simplify each term.

Tap for more steps...

Step 1.4.3.1.1.9.3.3.1

Rewrite $i^{2}$ as $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 - 36 \cdot - 1}$

Step 1.4.3.1.1.9.3.3.2

Multiply $- 36$ by $- 1$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{1 + 36}$

Step 1.4.3.1.1.9.3.4

Add $1$ and $36$ .

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72 - 12 i}{37}$

Step 1.4.3.1.1.10

Split the fraction $\frac{- 72 - 12 i}{37}$ into two fractions.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} + \frac{- 72}{37} + \frac{- 12 i}{37}$

Step 1.4.3.1.1.11

Simplify each term.

Tap for more steps...

Step 1.4.3.1.1.11.1

Move the negative in front of the fraction.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} - \frac{72}{37} + \frac{- 12 i}{37}$

Step 1.4.3.1.1.11.2

Move the negative in front of the fraction.

$y = - \frac{16}{37} + \frac{96 i}{37} + \frac{2 x (1 - 6 i)}{37} - \frac{72}{37} - \frac{12 i}{37}$

Step 1.4.3.1.2

Combine the numerators over the common denominator.

$y = \frac{- 16 + 96 i + 2 x (1 - 6 i) - 72 - 12 i}{37}$

Step 1.4.3.1.3

Simplify each term.

Tap for more steps...

Step 1.4.3.1.3.1

Apply the distributive property.

$y = \frac{- 16 + 96 i + 2 x \cdot 1 + 2 x (- 6 i) - 72 - 12 i}{37}$

Step 1.4.3.1.3.2

Multiply $2$ by $1$ .

$y = \frac{- 16 + 96 i + 2 x + 2 x (- 6 i) - 72 - 12 i}{37}$

Step 1.4.3.1.3.3

Multiply $- 6$ by $2$ .

$y = \frac{- 16 + 96 i + 2 x - 12 x i - 72 - 12 i}{37}$

Step 1.4.3.1.4

Simplify by adding terms.

Tap for more steps...

Step 1.4.3.1.4.1

Subtract $72$ from $- 16$ .

$y = \frac{96 i + 2 x - 12 x i - 88 - 12 i}{37}$

Step 1.4.3.1.4.2

Subtract $12 i$ from $96 i$ .

$y = \frac{2 x - 12 x i - 88 + 84 i}{37}$

Step 1.4.3.2

Simplify the numerator.

Tap for more steps...

Step 1.4.3.2.1

Factor $2$ out of $2 x - 12 x i - 88 + 84 i$ .

Tap for more steps...

Step 1.4.3.2.1.1

Factor $2$ out of $2 x$ .

$y = \frac{2 (x) - 12 x i - 88 + 84 i}{37}$

Step 1.4.3.2.1.2

Factor $2$ out of $- 12 x i$ .

$y = \frac{2 (x) + 2 (- 6 x i) - 88 + 84 i}{37}$

Step 1.4.3.2.1.3

Factor $2$ out of $- 88$ .

$y = \frac{2 x + 2 (- 6 x i) + 2 \cdot - 44 + 84 i}{37}$

Step 1.4.3.2.1.4

Factor $2$ out of $84 i$ .

$y = \frac{2 x + 2 (- 6 x i) + 2 \cdot - 44 + 2 (42 i)}{37}$

Step 1.4.3.2.1.5

Factor $2$ out of $2 x + 2 (- 6 x i)$ .

$y = \frac{2 (x - 6 x i) + 2 \cdot - 44 + 2 (42 i)}{37}$

Step 1.4.3.2.1.6

Factor $2$ out of $2 (x - 6 x i) + 2 \cdot - 44$ .

$y = \frac{2 (x - 6 x i - 44) + 2 (42 i)}{37}$

Step 1.4.3.2.1.7

Factor $2$ out of $2 (x - 6 x i - 44) + 2 (42 i)$ .

$y = \frac{2 (x - 6 x i - 44 + 42 i)}{37}$

Step 1.4.3.2.2

Reorder terms.

$y = \frac{2 (- 6 i x + x - 44 + 42 i)}{37}$

Step 1.4.3.3

Simplify with factoring out.

Tap for more steps...

Step 1.4.3.3.1

Factor $- 1$ out of $- 6 i x$ .

$y = \frac{2 (- (6 i x) + x - 44 + 42 i)}{37}$

Step 1.4.3.3.2

Factor $- 1$ out of $x$ .

$y = \frac{2 (- (6 i x) - 1 (- x) - 44 + 42 i)}{37}$

Step 1.4.3.3.3

Factor $- 1$ out of $- (6 i x) - 1 (- x)$ .

$y = \frac{2 (- (6 i x - x) - 44 + 42 i)}{37}$

Step 1.4.3.3.4

Rewrite $- 44$ as $- 1 (44)$ .

$y = \frac{2 (- (6 i x - x) - 1 (44) + 42 i)}{37}$

Step 1.4.3.3.5

Factor $- 1$ out of $- (6 i x - x) - 1 (44)$ .

$y = \frac{2 (- (6 i x - x + 44) + 42 i)}{37}$

Step 1.4.3.3.6

Factor $- 1$ out of $42 i$ .

$y = \frac{2 (- (6 i x - x + 44) - (- 42 i))}{37}$

Step 1.4.3.3.7

Factor $- 1$ out of $- (6 i x - x + 44) - (- 42 i)$ .

$y = \frac{2 (- (6 i x - x + 44 - 42 i))}{37}$

Step 1.4.3.3.8

Simplify the expression.

Tap for more steps...

Step 1.4.3.3.8.1

Rewrite $- (6 i x - x + 44 - 42 i)$ as $- 1 (6 i x - x + 44 - 42 i)$ .

$y = \frac{2 (- 1 (6 i x - x + 44 - 42 i))}{37}$

Step 1.4.3.3.8.2

Move the negative in front of the fraction.

$y = - \frac{2 (6 i x - x + 44 - 42 i)}{37}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

Tap for more steps...

Step 3.1

Multiply $6 i$ by $0$ .

$y = - \frac{2 (6 i \cdot 0 - (0) + 44 - 42 i)}{37}$

Step 3.2

Remove parentheses.

$y = - \frac{2 (6 i (0) - (0) + 44 - 42 i)}{37}$

Step 3.3

Simplify the numerator.

Tap for more steps...

Step 3.3.1

Multiply $0$ by $6$ .

$y = - \frac{2 (0 i - (0) + 44 - 42 i)}{37}$

Step 3.3.2

Multiply $0$ by $i$ .

$y = - \frac{2 (0 - (0) + 44 - 42 i)}{37}$

Step 3.3.3

Multiply $- 1$ by $0$ .

$y = - \frac{2 (0 + 0 + 44 - 42 i)}{37}$

Step 3.3.4

Add $0$ and $0$ .

$y = - \frac{2 (0 + 44 - 42 i)}{37}$

Step 3.3.5

Add $0$ and $44$ .

$y = - \frac{2 (44 - 42 i)}{37}$

Step 3.4

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{2 (44 - 42 i)}{37})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Tap for more steps...

Step 4.1

Multiply $6 i$ by $1$ .

$y = - \frac{2 (6 i \cdot 1 - (1) + 44 - 42 i)}{37}$

Step 4.2

Remove parentheses.

$y = - \frac{2 (6 i (1) - (1) + 44 - 42 i)}{37}$

Step 4.3

Simplify the numerator.

Tap for more steps...

Step 4.3.1

Multiply $6$ by $1$ .

$y = - \frac{2 (6 i - (1) + 44 - 42 i)}{37}$

Step 4.3.2

Multiply $- 1$ by $1$ .

$y = - \frac{2 (6 i - 1 + 44 - 42 i)}{37}$

Step 4.3.3

Subtract $42 i$ from $6 i$ .

$y = - \frac{2 (- 1 + 44 - 36 i)}{37}$

Step 4.3.4

Add $- 1$ and $44$ .

$y = - \frac{2 (43 - 36 i)}{37}$

Step 4.4

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{2 (43 - 36 i)}{37})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Tap for more steps...

Step 5.1

Multiply $6 i$ by $2$ .

$y = - \frac{2 (6 i \cdot 2 - (2) + 44 - 42 i)}{37}$

Step 5.2

Remove parentheses.

$y = - \frac{2 (6 i (2) - (2) + 44 - 42 i)}{37}$

Step 5.3

Simplify the numerator.

Tap for more steps...

Step 5.3.1

Multiply $2$ by $6$ .

$y = - \frac{2 (12 i - (2) + 44 - 42 i)}{37}$

Step 5.3.2

Multiply $- 1$ by $2$ .

$y = - \frac{2 (12 i - 2 + 44 - 42 i)}{37}$

Step 5.3.3

Subtract $42 i$ from $12 i$ .

$y = - \frac{2 (- 2 + 44 - 30 i)}{37}$

Step 5.3.4

Add $- 2$ and $44$ .

$y = - \frac{2 (42 - 30 i)}{37}$

Step 5.4

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{2 (42 - 30 i)}{37})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{2 (44 - 42 i)}{37}), (1, - \frac{2 (43 - 36 i)}{37}), (2, - \frac{2 (42 - 30 i)}{37})$

Step 7