Solve for v -4(v+3)-3v=2(v+3)

$- 4 (v + 3) - 3 v = 2 (v + 3)$

Step 1

Simplify $- 4 (v + 3) - 3 v$ .

Simplify each term.

Apply the distributive property.

$- 4 v - 4 \cdot 3 - 3 v = 2 (v + 3)$

Multiply $- 4$ by $3$ .

$- 4 v - 12 - 3 v = 2 (v + 3)$

Subtract $3 v$ from $- 4 v$ .

$- 7 v - 12 = 2 (v + 3)$

Step 2

Simplify $2 (v + 3)$ .

Apply the distributive property.

$- 7 v - 12 = 2 v + 2 \cdot 3$

Multiply $2$ by $3$ .

$- 7 v - 12 = 2 v + 6$

Step 3

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

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

$- 7 v - 12 - 2 v = 6$

Subtract $2 v$ from $- 7 v$ .

$- 9 v - 12 = 6$

Step 4

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

Add $12$ to both sides of the equation.

$- 9 v = 6 + 12$

Add $6$ and $12$ .

$- 9 v = 18$

Step 5

Divide each term in $- 9 v = 18$ by $- 9$ and simplify.

Divide each term in $- 9 v = 18$ by $- 9$ .

$\frac{- 9 v}{- 9} = \frac{18}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 v}{- 9} = \frac{18}{- 9}$

Divide $v$ by $1$ .

$v = \frac{18}{- 9}$

Simplify the right side.

Divide $18$ by $- 9$ .

$v = - 2$