Solve for n -6(-n+19)=-(-12+12n)

$- 6 (- n + 19) = - (- 12 + 12 n)$

Step 1

Simplify $- 6 (- n + 19)$ .

Rewrite.

$0 + 0 - 6 (- n + 19) = - (- 12 + 12 n)$

Simplify by adding zeros.

$- 6 (- n + 19) = - (- 12 + 12 n)$

Apply the distributive property.

$- 6 (- n) - 6 \cdot 19 = - (- 12 + 12 n)$

Multiply.

Multiply $- 1$ by $- 6$ .

$6 n - 6 \cdot 19 = - (- 12 + 12 n)$

Multiply $- 6$ by $19$ .

$6 n - 114 = - (- 12 + 12 n)$

Step 2

Simplify $- (- 12 + 12 n)$ .

Apply the distributive property.

$6 n - 114 = - - 12 - (12 n)$

Multiply.

Multiply $- 1$ by $- 12$ .

$6 n - 114 = 12 - (12 n)$

Multiply $12$ by $- 1$ .

$6 n - 114 = 12 - 12 n$

Step 3

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

Add $12 n$ to both sides of the equation.

$6 n - 114 + 12 n = 12$

Add $6 n$ and $12 n$ .

$18 n - 114 = 12$

Step 4

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

Add $114$ to both sides of the equation.

$18 n = 12 + 114$

Add $12$ and $114$ .

$18 n = 126$

Step 5

Divide each term in $18 n = 126$ by $18$ and simplify.

Divide each term in $18 n = 126$ by $18$ .

$\frac{18 n}{18} = \frac{126}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 n}{18} = \frac{126}{18}$

Divide $n$ by $1$ .

$n = \frac{126}{18}$

Simplify the right side.

Divide $126$ by $18$ .

$n = 7$

Solve for n -6(-n+19)=-(-12+12n)

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