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

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

Simplify $3 (- y + 7)$ .

Rewrite.

$0 + 0 + 3 (- y + 7) = 3 (y + 5) + 6$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $- 1$ by $3$ .

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

Multiply $3$ by $7$ .

$- 3 y + 21 = 3 (y + 5) + 6$

Simplify $3 (y + 5) + 6$ .

Simplify each term.

Apply the distributive property.

$- 3 y + 21 = 3 y + 3 \cdot 5 + 6$

Multiply $3$ by $5$ .

$- 3 y + 21 = 3 y + 15 + 6$

Add $15$ and $6$ .

$- 3 y + 21 = 3 y + 21$

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

Subtract $3 y$ from both sides of the equation.

$- 3 y + 21 - 3 y = 21$

Subtract $3 y$ from $- 3 y$ .

$- 6 y + 21 = 21$

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

Subtract $21$ from both sides of the equation.

$- 6 y = 21 - 21$

Subtract $21$ from $21$ .

$- 6 y = 0$

Divide each term in $- 6 y = 0$ by $- 6$ and simplify.

Divide each term in $- 6 y = 0$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Divide $y$ by $1$ .

$y = \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$y = 0$