Simplify (2x)/3(12x+18)

$\frac{2 x}{3} (12 x + 18)$

Simplify terms.

Apply the distributive property.

$\frac{2 x}{3} (12 x) + \frac{2 x}{3} \cdot 18$

Rewrite using the commutative property of multiplication.

$12 \frac{2 x}{3} x + \frac{2 x}{3} \cdot 18$

Cancel the common factor of $3$ .

Factor $3$ out of $18$ .

$12 \frac{2 x}{3} x + \frac{2 x}{3} \cdot (3 (6))$

Cancel the common factor.

$12 \frac{2 x}{3} x + \frac{2 x}{3} \cdot (3 \cdot 6)$

Rewrite the expression.

$12 \frac{2 x}{3} x + 2 x \cdot 6$

Multiply $6$ by $2$ .

$12 \frac{2 x}{3} x + 12 x$

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$3 (4) \frac{2 x}{3} x + 12 x$

Cancel the common factor.

$3 \cdot 4 \frac{2 x}{3} x + 12 x$

Rewrite the expression.

$4 (2 x) x + 12 x$

Multiply $2$ by $4$ .

$8 x \cdot x + 12 x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$8 (x \cdot x) + 12 x$

Multiply $x$ by $x$ .

$8 x^{2} + 12 x$