Solve for v 5v-6=-3(-2v+7)

$5 v - 6 = - 3 (- 2 v + 7)$

Step 1

Simplify $- 3 (- 2 v + 7)$ .

Rewrite.

$5 v - 6 = 0 + 0 - 3 (- 2 v + 7)$

Simplify by adding zeros.

$5 v - 6 = - 3 (- 2 v + 7)$

Apply the distributive property.

$5 v - 6 = - 3 (- 2 v) - 3 \cdot 7$

Multiply.

Multiply $- 2$ by $- 3$ .

$5 v - 6 = 6 v - 3 \cdot 7$

Multiply $- 3$ by $7$ .

$5 v - 6 = 6 v - 21$

Step 2

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

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

$5 v - 6 - 6 v = - 21$

Subtract $6 v$ from $5 v$ .

$- v - 6 = - 21$

Step 3

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

Add $6$ to both sides of the equation.

$- v = - 21 + 6$

Add $- 21$ and $6$ .

$- v = - 15$

Step 4

Divide each term in $- v = - 15$ by $- 1$ and simplify.

Divide each term in $- v = - 15$ by $- 1$ .

$\frac{- v}{- 1} = \frac{- 15}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{v}{1} = \frac{- 15}{- 1}$

Divide $v$ by $1$ .

$v = \frac{- 15}{- 1}$

Simplify the right side.

Divide $- 15$ by $- 1$ .

$v = 15$