Solve for n -5n+6=-7(5n-6)-6n

$- 5 n + 6 = - 7 (5 n - 6) - 6 n$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 7 (5 n - 6) - 6 n = - 5 n + 6$

Step 2

Simplify $- 7 (5 n - 6) - 6 n$ .

Simplify each term.

Apply the distributive property.

$- 7 (5 n) - 7 \cdot - 6 - 6 n = - 5 n + 6$

Multiply $5$ by $- 7$ .

$- 35 n - 7 \cdot - 6 - 6 n = - 5 n + 6$

Multiply $- 7$ by $- 6$ .

$- 35 n + 42 - 6 n = - 5 n + 6$

Subtract $6 n$ from $- 35 n$ .

$- 41 n + 42 = - 5 n + 6$

Step 3

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

Add $5 n$ to both sides of the equation.

$- 41 n + 42 + 5 n = 6$

Add $- 41 n$ and $5 n$ .

$- 36 n + 42 = 6$

Step 4

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

Subtract $42$ from both sides of the equation.

$- 36 n = 6 - 42$

Subtract $42$ from $6$ .

$- 36 n = - 36$

Step 5

Divide each term in $- 36 n = - 36$ by $- 36$ and simplify.

Divide each term in $- 36 n = - 36$ by $- 36$ .

$\frac{- 36 n}{- 36} = \frac{- 36}{- 36}$

Simplify the left side.

Cancel the common factor of $- 36$ .

Cancel the common factor.

$\frac{- 36 n}{- 36} = \frac{- 36}{- 36}$

Divide $n$ by $1$ .

$n = \frac{- 36}{- 36}$

Simplify the right side.

Divide $- 36$ by $- 36$ .

$n = 1$