Solve for n (8n-(-2))/7=6

$\frac{8 n - (- 2)}{7} = 6$

Step 1

Multiply both sides by $7$ .

$\frac{8 n - (- 2)}{7} \cdot 7 = 6 \cdot 7$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{8 n - (- 2)}{7} \cdot 7$ .

Simplify the numerator.

Multiply $- 1$ by $- 2$ .

$\frac{8 n + 2}{7} \cdot 7 = 6 \cdot 7$

Factor $2$ out of $8 n + 2$ .

Factor $2$ out of $8 n$ .

$\frac{2 (4 n) + 2}{7} \cdot 7 = 6 \cdot 7$

Factor $2$ out of $2$ .

$\frac{2 (4 n) + 2 (1)}{7} \cdot 7 = 6 \cdot 7$

Factor $2$ out of $2 (4 n) + 2 (1)$ .

$\frac{2 (4 n + 1)}{7} \cdot 7 = 6 \cdot 7$

Simplify terms.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{2 (4 n + 1)}{7} \cdot 7 = 6 \cdot 7$

Rewrite the expression.

$2 (4 n + 1) = 6 \cdot 7$

Apply the distributive property.

$2 (4 n) + 2 \cdot 1 = 6 \cdot 7$

Multiply.

Multiply $4$ by $2$ .

$8 n + 2 \cdot 1 = 6 \cdot 7$

Multiply $2$ by $1$ .

$8 n + 2 = 6 \cdot 7$

Simplify the right side.

Multiply $6$ by $7$ .

$8 n + 2 = 42$

Step 3

Solve for $n$ .

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

Subtract $2$ from both sides of the equation.

$8 n = 42 - 2$

Subtract $2$ from $42$ .

$8 n = 40$

Divide each term in $8 n = 40$ by $8$ and simplify.

Divide each term in $8 n = 40$ by $8$ .

$\frac{8 n}{8} = \frac{40}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 n}{8} = \frac{40}{8}$

Divide $n$ by $1$ .

$n = \frac{40}{8}$

Simplify the right side.

Divide $40$ by $8$ .

$n = 5$

Solve for n (8n-(-2))/7=6

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