Solve for v -6(2v+4)=-8(v-4)

$- 6 (2 v + 4) = - 8 (v - 4)$

Step 1

Simplify $- 6 (2 v + 4)$ .

Start simplifying.

$0 + 0 - 6 (2 v + 4) = - 8 (v - 4)$

Simplify by adding zeros.

$- 6 (2 v + 4) = - 8 (v - 4)$

Apply the distributive property.

$- 6 (2 v) - 6 \cdot 4 = - 8 (v - 4)$

Multiply.

Multiply $2$ by $- 6$ .

$- 12 v - 6 \cdot 4 = - 8 (v - 4)$

Multiply $- 6$ by $4$ .

$- 12 v - 24 = - 8 (v - 4)$

Step 2

Simplify $- 8 (v - 4)$ .

Apply the distributive property.

$- 12 v - 24 = - 8 v - 8 \cdot - 4$

Multiply $- 8$ by $- 4$ .

$- 12 v - 24 = - 8 v + 32$

Step 3

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

Add $8 v$ to both sides of the equation.

$- 12 v - 24 + 8 v = 32$

Add $- 12 v$ and $8 v$ .

$- 4 v - 24 = 32$

Step 4

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

Add $24$ to both sides of the equation.

$- 4 v = 32 + 24$

Add $32$ and $24$ .

$- 4 v = 56$

Step 5

Divide each term in $- 4 v = 56$ by $- 4$ and simplify.

Divide each term in $- 4 v = 56$ by $- 4$ .

$\frac{- 4 v}{- 4} = \frac{56}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 v}{- 4} = \frac{56}{- 4}$

Divide $v$ by $1$ .

$v = \frac{56}{- 4}$

Simplify the right side.

Divide $56$ by $- 4$ .

$v = - 14$