Solve for y 2y-3(2y-3)+2=31

$2 y - 3 (2 y - 3) + 2 = 31$

Step 1

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

Simplify each term.

Apply the distributive property.

$2 y - 3 (2 y) - 3 \cdot - 3 + 2 = 31$

Multiply $2$ by $- 3$ .

$2 y - 6 y - 3 \cdot - 3 + 2 = 31$

Multiply $- 3$ by $- 3$ .

$2 y - 6 y + 9 + 2 = 31$

Simplify by adding terms.

Subtract $6 y$ from $2 y$ .

$- 4 y + 9 + 2 = 31$

Add $9$ and $2$ .

$- 4 y + 11 = 31$

Step 2

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

Subtract $11$ from both sides of the equation.

$- 4 y = 31 - 11$

Subtract $11$ from $31$ .

$- 4 y = 20$

Step 3

Divide each term in $- 4 y = 20$ by $- 4$ and simplify.

Divide each term in $- 4 y = 20$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{20}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{20}{- 4}$

Divide $y$ by $1$ .

$y = \frac{20}{- 4}$

Simplify the right side.

Divide $20$ by $- 4$ .

$y = - 5$