Solve for n -12=-6(-8n+6)+8(-4+n)

$- 12 = - 6 (- 8 n + 6) + 8 (- 4 + n)$

Step 1

Rewrite the equation as $- 6 (- 8 n + 6) + 8 (- 4 + n) = - 12$ .

$- 6 (- 8 n + 6) + 8 (- 4 + n) = - 12$

Step 2

Simplify $- 6 (- 8 n + 6) + 8 (- 4 + n)$ .

Simplify each term.

Apply the distributive property.

$- 6 (- 8 n) - 6 \cdot 6 + 8 (- 4 + n) = - 12$

Multiply $- 8$ by $- 6$ .

$48 n - 6 \cdot 6 + 8 (- 4 + n) = - 12$

Multiply $- 6$ by $6$ .

$48 n - 36 + 8 (- 4 + n) = - 12$

Apply the distributive property.

$48 n - 36 + 8 \cdot - 4 + 8 n = - 12$

Multiply $8$ by $- 4$ .

$48 n - 36 - 32 + 8 n = - 12$

Simplify by adding terms.

Add $48 n$ and $8 n$ .

$56 n - 36 - 32 = - 12$

Subtract $32$ from $- 36$ .

$56 n - 68 = - 12$

Step 3

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

Add $68$ to both sides of the equation.

$56 n = - 12 + 68$

Add $- 12$ and $68$ .

$56 n = 56$

Step 4

Divide each term in $56 n = 56$ by $56$ and simplify.

Divide each term in $56 n = 56$ by $56$ .

$\frac{56 n}{56} = \frac{56}{56}$

Simplify the left side.

Cancel the common factor of $56$ .

Cancel the common factor.

$\frac{56 n}{56} = \frac{56}{56}$

Divide $n$ by $1$ .

$n = \frac{56}{56}$

Simplify the right side.

Divide $56$ by $56$ .

$n = 1$