Basic Math Examples

$2 z (4 y + 9) - 3 y = 11$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 z (4 y) + 2 z \cdot 9 - 3 y = 11$

Step 1.2

Rewrite using the commutative property of multiplication.

$2 \cdot 4 z y + 2 z \cdot 9 - 3 y = 11$

Step 1.3

Multiply $9$ by $2$ .

$2 \cdot 4 z y + 18 z - 3 y = 11$

Step 1.4

Multiply $2$ by $4$ .

$8 z y + 18 z - 3 y = 11$

Step 2

Subtract $18 z$ from both sides of the equation.

$8 z y - 3 y = 11 - 18 z$

Step 3

Factor $y$ out of $8 z y - 3 y$ .

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Step 3.1

Factor $y$ out of $8 z y$ .

$y (8 z) - 3 y = 11 - 18 z$

Step 3.2

Factor $y$ out of $- 3 y$ .

$y (8 z) + y \cdot - 3 = 11 - 18 z$

Step 3.3

Factor $y$ out of $y (8 z) + y \cdot - 3$ .

$y (8 z - 3) = 11 - 18 z$

Step 4

Divide each term in $y (8 z - 3) = 11 - 18 z$ by $8 z - 3$ and simplify.

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Step 4.1

Divide each term in $y (8 z - 3) = 11 - 18 z$ by $8 z - 3$ .

$\frac{y (8 z - 3)}{8 z - 3} = \frac{11}{8 z - 3} + \frac{- 18 z}{8 z - 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8 z - 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{y (8 z - 3)}{8 z - 3} = \frac{11}{8 z - 3} + \frac{- 18 z}{8 z - 3}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{11}{8 z - 3} + \frac{- 18 z}{8 z - 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$y = \frac{11 - 18 z}{8 z - 3}$