Solve for y 12(5+2y)=4y-(6-9y)

$12 (5 + 2 y) = 4 y - (6 - 9 y)$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 y - (6 - 9 y) = 12 (5 + 2 y)$

Step 2

Simplify $4 y - (6 - 9 y)$ .

Simplify each term.

Apply the distributive property.

$4 y - 1 \cdot 6 - (- 9 y) = 12 (5 + 2 y)$

Multiply $- 1$ by $6$ .

$4 y - 6 - (- 9 y) = 12 (5 + 2 y)$

Multiply $- 9$ by $- 1$ .

$4 y - 6 + 9 y = 12 (5 + 2 y)$

Add $4 y$ and $9 y$ .

$13 y - 6 = 12 (5 + 2 y)$

Step 3

Simplify $12 (5 + 2 y)$ .

Apply the distributive property.

$13 y - 6 = 12 \cdot 5 + 12 (2 y)$

Multiply.

Multiply $12$ by $5$ .

$13 y - 6 = 60 + 12 (2 y)$

Multiply $2$ by $12$ .

$13 y - 6 = 60 + 24 y$

Step 4

Move all terms containing $y$ to the left side of the equation.

Subtract $24 y$ from both sides of the equation.

$13 y - 6 - 24 y = 60$

Subtract $24 y$ from $13 y$ .

$- 11 y - 6 = 60$

Step 5

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

Add $6$ to both sides of the equation.

$- 11 y = 60 + 6$

Add $60$ and $6$ .

$- 11 y = 66$

Step 6

Divide each term in $- 11 y = 66$ by $- 11$ and simplify.

Divide each term in $- 11 y = 66$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{66}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{66}{- 11}$

Divide $y$ by $1$ .

$y = \frac{66}{- 11}$

Simplify the right side.

Divide $66$ by $- 11$ .

$y = - 6$

Solve for y 12(5+2y)=4y-(6-9y)

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