Solve by Factoring 4(y-3)-6y=-2(y+6)

$4 (y - 3) - 6 y = - 2 (y + 6)$

Step 1

Add $2 (y + 6)$ to both sides of the equation.

$4 (y - 3) - 6 y + 2 (y + 6) = 0$

Step 2

Simplify $4 (y - 3) - 6 y + 2 (y + 6)$ .

Simplify each term.

Apply the distributive property.

$4 y + 4 \cdot - 3 - 6 y + 2 (y + 6) = 0$

Multiply $4$ by $- 3$ .

$4 y - 12 - 6 y + 2 (y + 6) = 0$

Apply the distributive property.

$4 y - 12 - 6 y + 2 y + 2 \cdot 6 = 0$

Multiply $2$ by $6$ .

$4 y - 12 - 6 y + 2 y + 12 = 0$

Combine the opposite terms in $4 y - 12 - 6 y + 2 y + 12$ .

Add $- 12$ and $12$ .

$4 y - 6 y + 2 y + 0 = 0$

Add $4 y - 6 y + 2 y$ and $0$ .

$4 y - 6 y + 2 y = 0$

Subtract $6 y$ from $4 y$ .

$- 2 y + 2 y = 0$

Add $- 2 y$ and $2 y$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true