Evaluate 6-4(3-5)^2+30/5

$6 - 4 {(3 - 5)}^{2} + \frac{30}{5}$

Step 1

Find the common denominator.

Write $6$ as a fraction with denominator $1$ .

$\frac{6}{1} - 4 {(3 - 5)}^{2} + \frac{30}{5}$

Multiply $\frac{6}{1}$ by $\frac{5}{5}$ .

$\frac{6}{1} \cdot \frac{5}{5} - 4 {(3 - 5)}^{2} + \frac{30}{5}$

Multiply $\frac{6}{1}$ by $\frac{5}{5}$ .

$\frac{6 \cdot 5}{5} - 4 {(3 - 5)}^{2} + \frac{30}{5}$

Write $- 4 {(3 - 5)}^{2}$ as a fraction with denominator $1$ .

$\frac{6 \cdot 5}{5} + \frac{- 4 {(3 - 5)}^{2}}{1} + \frac{30}{5}$

Multiply $\frac{- 4 {(3 - 5)}^{2}}{1}$ by $\frac{5}{5}$ .

$\frac{6 \cdot 5}{5} + \frac{- 4 {(3 - 5)}^{2}}{1} \cdot \frac{5}{5} + \frac{30}{5}$

Multiply $\frac{- 4 {(3 - 5)}^{2}}{1}$ by $\frac{5}{5}$ .

$\frac{6 \cdot 5}{5} + \frac{- 4 {(3 - 5)}^{2} \cdot 5}{5} + \frac{30}{5}$

Step 2

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 - 4 {(3 - 5)}^{2} \cdot 5 + 30}{5}$

Step 3

Simplify each term.

Multiply $6$ by $5$ .

$\frac{30 - 4 {(3 - 5)}^{2} \cdot 5 + 30}{5}$

Subtract $5$ from $3$ .

$\frac{30 - 4 {(- 2)}^{2} \cdot 5 + 30}{5}$

Raise $- 2$ to the power of $2$ .

$\frac{30 - 4 \cdot 4 \cdot 5 + 30}{5}$

Multiply $- 4 \cdot 4 \cdot 5$ .

Multiply $- 4$ by $4$ .

$\frac{30 - 16 \cdot 5 + 30}{5}$

Multiply $- 16$ by $5$ .

$\frac{30 - 80 + 30}{5}$

Step 4

Simplify the expression.

Subtract $80$ from $30$ .

$\frac{- 50 + 30}{5}$

Add $- 50$ and $30$ .

$\frac{- 20}{5}$

Divide $- 20$ by $5$ .

$- 4$