Evaluate 9q^2-2/3(3q-7)+5q^2

$9 q^{2} - \frac{2}{3} (3 q - 7) + 5 q^{2}$

Step 1

Simplify each term.

Apply the distributive property.

$9 q^{2} - \frac{2}{3} (3 q) - \frac{2}{3} \cdot - 7 + 5 q^{2}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$9 q^{2} + \frac{- 2}{3} (3 q) - \frac{2}{3} \cdot - 7 + 5 q^{2}$

Factor $3$ out of $3 q$ .

$9 q^{2} + \frac{- 2}{3} (3 (q)) - \frac{2}{3} \cdot - 7 + 5 q^{2}$

Cancel the common factor.

$9 q^{2} + \frac{- 2}{3} (3 q) - \frac{2}{3} \cdot - 7 + 5 q^{2}$

Rewrite the expression.

$9 q^{2} - 2 q - \frac{2}{3} \cdot - 7 + 5 q^{2}$

Multiply $- \frac{2}{3} \cdot - 7$ .

Multiply $- 7$ by $- 1$ .

$9 q^{2} - 2 q + 7 (\frac{2}{3}) + 5 q^{2}$

Combine $7$ and $\frac{2}{3}$ .

$9 q^{2} - 2 q + \frac{7 \cdot 2}{3} + 5 q^{2}$

Multiply $7$ by $2$ .

$9 q^{2} - 2 q + \frac{14}{3} + 5 q^{2}$

Step 2

Add $9 q^{2}$ and $5 q^{2}$ .

$14 q^{2} - 2 q + \frac{14}{3}$