Solve for n 3(n-9)-2(n+4)=6n

$3 (n - 9) - 2 (n + 4) = 6 n$

Step 1

Simplify $3 (n - 9) - 2 (n + 4)$ .

Simplify each term.

Apply the distributive property.

$3 n + 3 \cdot - 9 - 2 (n + 4) = 6 n$

Multiply $3$ by $- 9$ .

$3 n - 27 - 2 (n + 4) = 6 n$

Apply the distributive property.

$3 n - 27 - 2 n - 2 \cdot 4 = 6 n$

Multiply $- 2$ by $4$ .

$3 n - 27 - 2 n - 8 = 6 n$

Simplify by adding terms.

Subtract $2 n$ from $3 n$ .

$n - 27 - 8 = 6 n$

Subtract $8$ from $- 27$ .

$n - 35 = 6 n$

Step 2

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

Subtract $6 n$ from both sides of the equation.

$n - 35 - 6 n = 0$

Subtract $6 n$ from $n$ .

$- 5 n - 35 = 0$

Step 3

Add $35$ to both sides of the equation.

$- 5 n = 35$

Step 4

Divide each term in $- 5 n = 35$ by $- 5$ and simplify.

Divide each term in $- 5 n = 35$ by $- 5$ .

$\frac{- 5 n}{- 5} = \frac{35}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 n}{- 5} = \frac{35}{- 5}$

Divide $n$ by $1$ .

$n = \frac{35}{- 5}$

Simplify the right side.

Divide $35$ by $- 5$ .

$n = - 7$