Find the Product -2/5(5-10e)=e+1/3(6e-12)

$- \frac{2}{5} (5 - 10 e) = e + \frac{1}{3} (6 e - 12)$

Step 1

Simplify terms.

Apply the distributive property.

$- \frac{2}{5} \cdot 5 - \frac{2}{5} (- 10 e) = e + \frac{1}{3} \cdot (6 e - 12)$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} \cdot 5 - \frac{2}{5} (- 10 e) = e + \frac{1}{3} \cdot (6 e - 12)$

Cancel the common factor.

$\frac{- 2}{5} \cdot 5 - \frac{2}{5} (- 10 e) = e + \frac{1}{3} \cdot (6 e - 12)$

Rewrite the expression.

$- 2 - \frac{2}{5} (- 10 e) = e + \frac{1}{3} \cdot (6 e - 12)$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- 2 + \frac{- 2}{5} (- 10 e) = e + \frac{1}{3} \cdot (6 e - 12)$

Factor $5$ out of $- 10 e$ .

$- 2 + \frac{- 2}{5} (5 (- 2 e)) = e + \frac{1}{3} \cdot (6 e - 12)$

Cancel the common factor.

$- 2 + \frac{- 2}{5} (5 (- 2 e)) = e + \frac{1}{3} \cdot (6 e - 12)$

Rewrite the expression.

$- 2 - 2 (- 2 e) = e + \frac{1}{3} \cdot (6 e - 12)$

Multiply $- 2$ by $- 2$ .

$- 2 + 4 e = e + \frac{1}{3} \cdot (6 e - 12)$

Step 2

Simplify each term.

Apply the distributive property.

$- 2 + 4 e = e + \frac{1}{3} (6 e) + \frac{1}{3} \cdot - 12$

Cancel the common factor of $3$ .

Factor $3$ out of $6 e$ .

$- 2 + 4 e = e + \frac{1}{3} (3 (2 e)) + \frac{1}{3} \cdot - 12$

Cancel the common factor.

$- 2 + 4 e = e + \frac{1}{3} (3 (2 e)) + \frac{1}{3} \cdot - 12$

Rewrite the expression.

$- 2 + 4 e = e + 2 e + \frac{1}{3} \cdot - 12$

Cancel the common factor of $3$ .

Factor $3$ out of $- 12$ .

$- 2 + 4 e = e + 2 e + \frac{1}{3} \cdot (3 (- 4))$

Cancel the common factor.

$- 2 + 4 e = e + 2 e + \frac{1}{3} \cdot (3 \cdot - 4)$

Rewrite the expression.

$- 2 + 4 e = e + 2 e - 4$

Step 3

Add $e$ and $2 e$ .

$- 2 + 4 e = 3 e - 4$