Solve for n 14+3n=8n-3(n-4)

$14 + 3 n = 8 n - 3 (n - 4)$

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.

$8 n - 3 (n - 4) = 14 + 3 n$

Step 2

Simplify $8 n - 3 (n - 4)$ .

Simplify each term.

Apply the distributive property.

$8 n - 3 n - 3 \cdot - 4 = 14 + 3 n$

Multiply $- 3$ by $- 4$ .

$8 n - 3 n + 12 = 14 + 3 n$

Subtract $3 n$ from $8 n$ .

$5 n + 12 = 14 + 3 n$

Step 3

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

Subtract $3 n$ from both sides of the equation.

$5 n + 12 - 3 n = 14$

Subtract $3 n$ from $5 n$ .

$2 n + 12 = 14$

Step 4

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

Subtract $12$ from both sides of the equation.

$2 n = 14 - 12$

Subtract $12$ from $14$ .

$2 n = 2$

Step 5

Divide each term in $2 n = 2$ by $2$ and simplify.

Divide each term in $2 n = 2$ by $2$ .

$\frac{2 n}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{2}{2}$

Divide $n$ by $1$ .

$n = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$n = 1$