Solve for v -2(v+6)-6v=4(v+3)

$- 2 (v + 6) - 6 v = 4 (v + 3)$

Step 1

Simplify $- 2 (v + 6) - 6 v$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 2$ by $6$ .

$- 2 v - 12 - 6 v = 4 (v + 3)$

Subtract $6 v$ from $- 2 v$ .

$- 8 v - 12 = 4 (v + 3)$

Step 2

Simplify $4 (v + 3)$ .

Apply the distributive property.

$- 8 v - 12 = 4 v + 4 \cdot 3$

Multiply $4$ by $3$ .

$- 8 v - 12 = 4 v + 12$

Step 3

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

Subtract $4 v$ from both sides of the equation.

$- 8 v - 12 - 4 v = 12$

Subtract $4 v$ from $- 8 v$ .

$- 12 v - 12 = 12$

Step 4

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

Add $12$ to both sides of the equation.

$- 12 v = 12 + 12$

Add $12$ and $12$ .

$- 12 v = 24$

Step 5

Divide each term in $- 12 v = 24$ by $- 12$ and simplify.

Divide each term in $- 12 v = 24$ by $- 12$ .

$\frac{- 12 v}{- 12} = \frac{24}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 v}{- 12} = \frac{24}{- 12}$

Divide $v$ by $1$ .

$v = \frac{24}{- 12}$

Simplify the right side.

Divide $24$ by $- 12$ .

$v = - 2$