Solve for y -3(-4-6y)+7(-y+5)=-8

$- 3 (- 4 - 6 y) + 7 (- y + 5) = - 8$

Step 1

Simplify $- 3 (- 4 - 6 y) + 7 (- y + 5)$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot - 4 - 3 (- 6 y) + 7 (- y + 5) = - 8$

Multiply $- 3$ by $- 4$ .

$12 - 3 (- 6 y) + 7 (- y + 5) = - 8$

Multiply $- 6$ by $- 3$ .

$12 + 18 y + 7 (- y + 5) = - 8$

Apply the distributive property.

$12 + 18 y + 7 (- y) + 7 \cdot 5 = - 8$

Multiply $- 1$ by $7$ .

$12 + 18 y - 7 y + 7 \cdot 5 = - 8$

Multiply $7$ by $5$ .

$12 + 18 y - 7 y + 35 = - 8$

Simplify by adding terms.

Add $12$ and $35$ .

$18 y - 7 y + 47 = - 8$

Subtract $7 y$ from $18 y$ .

$11 y + 47 = - 8$

Step 2

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

Subtract $47$ from both sides of the equation.

$11 y = - 8 - 47$

Subtract $47$ from $- 8$ .

$11 y = - 55$

Step 3

Divide each term in $11 y = - 55$ by $11$ and simplify.

Divide each term in $11 y = - 55$ by $11$ .

$\frac{11 y}{11} = \frac{- 55}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{- 55}{11}$

Divide $y$ by $1$ .

$y = \frac{- 55}{11}$

Simplify the right side.

Divide $- 55$ by $11$ .

$y = - 5$