Solve for n 82n+26+74n=59+9(27n+93)

$82 n + 26 + 74 n = 59 + 9 (27 n + 93)$

Step 1

Add $82 n$ and $74 n$ .

$156 n + 26 = 59 + 9 (27 n + 93)$

Step 2

Simplify $59 + 9 (27 n + 93)$ .

Simplify each term.

Apply the distributive property.

$156 n + 26 = 59 + 9 (27 n) + 9 \cdot 93$

Multiply $27$ by $9$ .

$156 n + 26 = 59 + 243 n + 9 \cdot 93$

Multiply $9$ by $93$ .

$156 n + 26 = 59 + 243 n + 837$

Add $59$ and $837$ .

$156 n + 26 = 243 n + 896$

Step 3

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

Subtract $243 n$ from both sides of the equation.

$156 n + 26 - 243 n = 896$

Subtract $243 n$ from $156 n$ .

$- 87 n + 26 = 896$

Step 4

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

Subtract $26$ from both sides of the equation.

$- 87 n = 896 - 26$

Subtract $26$ from $896$ .

$- 87 n = 870$

Step 5

Divide each term in $- 87 n = 870$ by $- 87$ and simplify.

Divide each term in $- 87 n = 870$ by $- 87$ .

$\frac{- 87 n}{- 87} = \frac{870}{- 87}$

Simplify the left side.

Cancel the common factor of $- 87$ .

Cancel the common factor.

$\frac{- 87 n}{- 87} = \frac{870}{- 87}$

Divide $n$ by $1$ .

$n = \frac{870}{- 87}$

Simplify the right side.

Divide $870$ by $- 87$ .

$n = - 10$