Solve for v 6(5-8v)+12=-54

$6 (5 - 8 v) + 12 = - 54$

Step 1

Simplify $6 (5 - 8 v) + 12$ .

Simplify each term.

Apply the distributive property.

$6 \cdot 5 + 6 (- 8 v) + 12 = - 54$

Multiply $6$ by $5$ .

$30 + 6 (- 8 v) + 12 = - 54$

Multiply $- 8$ by $6$ .

$30 - 48 v + 12 = - 54$

Add $30$ and $12$ .

$- 48 v + 42 = - 54$

Step 2

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

Subtract $42$ from both sides of the equation.

$- 48 v = - 54 - 42$

Subtract $42$ from $- 54$ .

$- 48 v = - 96$

Step 3

Divide each term in $- 48 v = - 96$ by $- 48$ and simplify.

Divide each term in $- 48 v = - 96$ by $- 48$ .

$\frac{- 48 v}{- 48} = \frac{- 96}{- 48}$

Simplify the left side.

Cancel the common factor of $- 48$ .

Cancel the common factor.

$\frac{- 48 v}{- 48} = \frac{- 96}{- 48}$

Divide $v$ by $1$ .

$v = \frac{- 96}{- 48}$

Simplify the right side.

Divide $- 96$ by $- 48$ .

$v = 2$