Solve for n 5n+34=-2(1-7n)

$5 n + 34 = - 2 (1 - 7 n)$

Step 1

Simplify $- 2 (1 - 7 n)$ .

Rewrite.

$5 n + 34 = 0 + 0 - 2 (1 - 7 n)$

Simplify by adding zeros.

$5 n + 34 = - 2 (1 - 7 n)$

Apply the distributive property.

$5 n + 34 = - 2 \cdot 1 - 2 (- 7 n)$

Multiply.

Multiply $- 2$ by $1$ .

$5 n + 34 = - 2 - 2 (- 7 n)$

Multiply $- 7$ by $- 2$ .

$5 n + 34 = - 2 + 14 n$

Step 2

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

Subtract $14 n$ from both sides of the equation.

$5 n + 34 - 14 n = - 2$

Subtract $14 n$ from $5 n$ .

$- 9 n + 34 = - 2$

Step 3

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

Subtract $34$ from both sides of the equation.

$- 9 n = - 2 - 34$

Subtract $34$ from $- 2$ .

$- 9 n = - 36$

Step 4

Divide each term in $- 9 n = - 36$ by $- 9$ and simplify.

Divide each term in $- 9 n = - 36$ by $- 9$ .

$\frac{- 9 n}{- 9} = \frac{- 36}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 n}{- 9} = \frac{- 36}{- 9}$

Divide $n$ by $1$ .

$n = \frac{- 36}{- 9}$

Simplify the right side.

Divide $- 36$ by $- 9$ .

$n = 4$