Solve for w 3(w-2)+5=2(3w-5)

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

Step 1

Simplify $3 (w - 2) + 5$ .

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

$3 w - 6 + 5 = 2 (3 w - 5)$

Add $- 6$ and $5$ .

$3 w - 1 = 2 (3 w - 5)$

Step 2

Simplify $2 (3 w - 5)$ .

Apply the distributive property.

$3 w - 1 = 2 (3 w) + 2 \cdot - 5$

Multiply.

Multiply $3$ by $2$ .

$3 w - 1 = 6 w + 2 \cdot - 5$

Multiply $2$ by $- 5$ .

$3 w - 1 = 6 w - 10$

Step 3

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

Subtract $6 w$ from both sides of the equation.

$3 w - 1 - 6 w = - 10$

Subtract $6 w$ from $3 w$ .

$- 3 w - 1 = - 10$

Step 4

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

Add $1$ to both sides of the equation.

$- 3 w = - 10 + 1$

Add $- 10$ and $1$ .

$- 3 w = - 9$

Step 5

Divide each term in $- 3 w = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 w = - 9$ by $- 3$ .

$\frac{- 3 w}{- 3} = \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 w}{- 3} = \frac{- 9}{- 3}$

Divide $w$ by $1$ .

$w = \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$w = 3$