Solve for n (3n)/2+3=15

$\frac{3 n}{2} + 3 = 15$

Step 1

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

Subtract $3$ from both sides of the equation.

$\frac{3 n}{2} = 15 - 3$

Subtract $3$ from $15$ .

$\frac{3 n}{2} = 12$

Step 2

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

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} \cdot 12$

Step 3

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} \cdot 12$

Rewrite the expression.

$\frac{1}{3} (3 n) = \frac{2}{3} \cdot 12$

Cancel the common factor of $3$ .

Factor $3$ out of $3 n$ .

$\frac{1}{3} (3 (n)) = \frac{2}{3} \cdot 12$

Cancel the common factor.

$\frac{1}{3} (3 n) = \frac{2}{3} \cdot 12$

Rewrite the expression.

$n = \frac{2}{3} \cdot 12$

Simplify the right side.

Simplify $\frac{2}{3} \cdot 12$ .

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$n = 2 \cdot 4$

Multiply $2$ by $4$ .

$n = 8$