Solve for y 4(y-2)-3y=2(y-6)

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $- 2$ .

$4 y - 8 - 3 y = 2 (y - 6)$

Subtract $3 y$ from $4 y$ .

$y - 8 = 2 (y - 6)$

Step 2

Simplify $2 (y - 6)$ .

Apply the distributive property.

$y - 8 = 2 y + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$y - 8 = 2 y - 12$

Step 3

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

Subtract $2 y$ from both sides of the equation.

$y - 8 - 2 y = - 12$

Subtract $2 y$ from $y$ .

$- y - 8 = - 12$

Step 4

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

Add $8$ to both sides of the equation.

$- y = - 12 + 8$

Add $- 12$ and $8$ .

$- y = - 4$

Step 5

Divide each term in $- y = - 4$ by $- 1$ and simplify.

Divide each term in $- y = - 4$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 4}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$y = 4$