Solve for q 10q+3q+5=2(q-3)

$10 q + 3 q + 5 = 2 (q - 3)$

Step 1

Add $10 q$ and $3 q$ .

$13 q + 5 = 2 (q - 3)$

Step 2

Simplify $2 (q - 3)$ .

Apply the distributive property.

$13 q + 5 = 2 q + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$13 q + 5 = 2 q - 6$

Step 3

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

Subtract $2 q$ from both sides of the equation.

$13 q + 5 - 2 q = - 6$

Subtract $2 q$ from $13 q$ .

$11 q + 5 = - 6$

Step 4

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

Subtract $5$ from both sides of the equation.

$11 q = - 6 - 5$

Subtract $5$ from $- 6$ .

$11 q = - 11$

Step 5

Divide each term in $11 q = - 11$ by $11$ and simplify.

Divide each term in $11 q = - 11$ by $11$ .

$\frac{11 q}{11} = \frac{- 11}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 q}{11} = \frac{- 11}{11}$

Divide $q$ by $1$ .

$q = \frac{- 11}{11}$

Simplify the right side.

Divide $- 11$ by $11$ .

$q = - 1$