Solve for n 2/3(n+6)=10

$\frac{2}{3} (n + 6) = 10$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (n + 6)) = \frac{3}{2} \cdot 10$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (n + 6))$ .

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} n + \frac{2}{3} \cdot 6) = \frac{3}{2} \cdot 10$

Combine $\frac{2}{3}$ and $n$ .

$\frac{3}{2} (\frac{2 n}{3} + \frac{2}{3} \cdot 6) = \frac{3}{2} \cdot 10$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{3}{2} (\frac{2 n}{3} + \frac{2}{3} \cdot (3 (2))) = \frac{3}{2} \cdot 10$

Cancel the common factor.

$\frac{3}{2} (\frac{2 n}{3} + \frac{2}{3} \cdot (3 \cdot 2)) = \frac{3}{2} \cdot 10$

Rewrite the expression.

$\frac{3}{2} (\frac{2 n}{3} + 2 \cdot 2) = \frac{3}{2} \cdot 10$

Multiply $2$ by $2$ .

$\frac{3}{2} (\frac{2 n}{3} + 4) = \frac{3}{2} \cdot 10$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 n}{3} + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 10$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 n}{3} + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 10$

Rewrite the expression.

$\frac{1}{2} (2 n) + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 10$

Cancel the common factor of $2$ .

Factor $2$ out of $2 n$ .

$\frac{1}{2} (2 (n)) + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 10$

Cancel the common factor.

$\frac{1}{2} (2 n) + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 10$

Rewrite the expression.

$n + \frac{3}{2} \cdot 4 = \frac{3}{2} \cdot 10$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$n + \frac{3}{2} \cdot (2 (2)) = \frac{3}{2} \cdot 10$

Cancel the common factor.

$n + \frac{3}{2} \cdot (2 \cdot 2) = \frac{3}{2} \cdot 10$

Rewrite the expression.

$n + 3 \cdot 2 = \frac{3}{2} \cdot 10$

Multiply $3$ by $2$ .

$n + 6 = \frac{3}{2} \cdot 10$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 10$ .

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$n + 6 = \frac{3}{2} \cdot (2 (5))$

Cancel the common factor.

$n + 6 = \frac{3}{2} \cdot (2 \cdot 5)$

Rewrite the expression.

$n + 6 = 3 \cdot 5$

Multiply $3$ by $5$ .

$n + 6 = 15$

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

Subtract $6$ from both sides of the equation.

$n = 15 - 6$

Subtract $6$ from $15$ .

$n = 9$

Solve for n 2/3(n+6)=10

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