Solve for w 9(w-4)-7w=5(3w-2)

$9 (w - 4) - 7 w = 5 (3 w - 2)$

Step 1

Simplify $9 (w - 4) - 7 w$ .

Simplify each term.

Apply the distributive property.

$9 w + 9 \cdot - 4 - 7 w = 5 (3 w - 2)$

Multiply $9$ by $- 4$ .

$9 w - 36 - 7 w = 5 (3 w - 2)$

Subtract $7 w$ from $9 w$ .

$2 w - 36 = 5 (3 w - 2)$

Step 2

Simplify $5 (3 w - 2)$ .

Apply the distributive property.

$2 w - 36 = 5 (3 w) + 5 \cdot - 2$

Multiply.

Multiply $3$ by $5$ .

$2 w - 36 = 15 w + 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$2 w - 36 = 15 w - 10$

Step 3

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

Subtract $15 w$ from both sides of the equation.

$2 w - 36 - 15 w = - 10$

Subtract $15 w$ from $2 w$ .

$- 13 w - 36 = - 10$

Step 4

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

Add $36$ to both sides of the equation.

$- 13 w = - 10 + 36$

Add $- 10$ and $36$ .

$- 13 w = 26$

Step 5

Divide each term in $- 13 w = 26$ by $- 13$ and simplify.

Divide each term in $- 13 w = 26$ by $- 13$ .

$\frac{- 13 w}{- 13} = \frac{26}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 w}{- 13} = \frac{26}{- 13}$

Divide $w$ by $1$ .

$w = \frac{26}{- 13}$

Simplify the right side.

Divide $26$ by $- 13$ .

$w = - 2$