Basic Math Examples

$9 x + 12 y + 15 z = 420$

Step 1

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

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Step 1.1

Subtract $9 x$ from both sides of the equation.

$12 y + 15 z = 420 - 9 x$

Step 1.2

Subtract $15 z$ from both sides of the equation.

$12 y = 420 - 9 x - 15 z$

Step 2

Divide each term in $12 y = 420 - 9 x - 15 z$ by $12$ and simplify.

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Step 2.1

Divide each term in $12 y = 420 - 9 x - 15 z$ by $12$ .

$\frac{12 y}{12} = \frac{420}{12} + \frac{- 9 x}{12} + \frac{- 15 z}{12}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{420}{12} + \frac{- 9 x}{12} + \frac{- 15 z}{12}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{420}{12} + \frac{- 9 x}{12} + \frac{- 15 z}{12}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $420$ by $12$ .

$y = 35 + \frac{- 9 x}{12} + \frac{- 15 z}{12}$

Step 2.3.1.2

Cancel the common factor of $- 9$ and $12$ .

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Step 2.3.1.2.1

Factor $3$ out of $- 9 x$ .

$y = 35 + \frac{3 (- 3 x)}{12} + \frac{- 15 z}{12}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $3$ out of $12$ .

$y = 35 + \frac{3 (- 3 x)}{3 (4)} + \frac{- 15 z}{12}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y = 35 + \frac{3 (- 3 x)}{3 \cdot 4} + \frac{- 15 z}{12}$

Step 2.3.1.2.2.3

Rewrite the expression.

$y = 35 + \frac{- 3 x}{4} + \frac{- 15 z}{12}$

Step 2.3.1.3

Move the negative in front of the fraction.

$y = 35 - \frac{3 x}{4} + \frac{- 15 z}{12}$

Step 2.3.1.4

Cancel the common factor of $- 15$ and $12$ .

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Step 2.3.1.4.1

Factor $3$ out of $- 15 z$ .

$y = 35 - \frac{3 x}{4} + \frac{3 (- 5 z)}{12}$

Step 2.3.1.4.2

Cancel the common factors.

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Step 2.3.1.4.2.1

Factor $3$ out of $12$ .

$y = 35 - \frac{3 x}{4} + \frac{3 (- 5 z)}{3 (4)}$

Step 2.3.1.4.2.2

Cancel the common factor.

$y = 35 - \frac{3 x}{4} + \frac{3 (- 5 z)}{3 \cdot 4}$

Step 2.3.1.4.2.3

Rewrite the expression.

$y = 35 - \frac{3 x}{4} + \frac{- 5 z}{4}$

Step 2.3.1.5

Move the negative in front of the fraction.

$y = 35 - \frac{3 x}{4} - \frac{5 z}{4}$