Solve for q 2(-2-5q)=-3(-4-2q)

$2 (- 2 - 5 q) = - 3 (- 4 - 2 q)$

Step 1

Simplify $2 (- 2 - 5 q)$ .

Start simplifying.

$0 + 0 + 2 (- 2 - 5 q) = - 3 (- 4 - 2 q)$

Simplify by adding zeros.

$2 (- 2 - 5 q) = - 3 (- 4 - 2 q)$

Apply the distributive property.

$2 \cdot - 2 + 2 (- 5 q) = - 3 (- 4 - 2 q)$

Multiply.

Multiply $2$ by $- 2$ .

$- 4 + 2 (- 5 q) = - 3 (- 4 - 2 q)$

Multiply $- 5$ by $2$ .

$- 4 - 10 q = - 3 (- 4 - 2 q)$

Step 2

Simplify $- 3 (- 4 - 2 q)$ .

Apply the distributive property.

$- 4 - 10 q = - 3 \cdot - 4 - 3 (- 2 q)$

Multiply.

Multiply $- 3$ by $- 4$ .

$- 4 - 10 q = 12 - 3 (- 2 q)$

Multiply $- 2$ by $- 3$ .

$- 4 - 10 q = 12 + 6 q$

Step 3

Move all terms containing $q$ to the left side of the equation.

Subtract $6 q$ from both sides of the equation.

$- 4 - 10 q - 6 q = 12$

Subtract $6 q$ from $- 10 q$ .

$- 4 - 16 q = 12$

Step 4

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

Add $4$ to both sides of the equation.

$- 16 q = 12 + 4$

Add $12$ and $4$ .

$- 16 q = 16$

Step 5

Divide each term in $- 16 q = 16$ by $- 16$ and simplify.

Divide each term in $- 16 q = 16$ by $- 16$ .

$\frac{- 16 q}{- 16} = \frac{16}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 q}{- 16} = \frac{16}{- 16}$

Divide $q$ by $1$ .

$q = \frac{16}{- 16}$

Simplify the right side.

Divide $16$ by $- 16$ .

$q = - 1$

Solve for q 2(-2-5q)=-3(-4-2q)

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