Solve for q 2(2q+1.5)=18-q

$2 (2 q + 1.5) = 18 - q$

Step 1

Simplify $2 (2 q + 1.5)$ .

Rewrite.

$0 + 0 + 2 (2 q + 1.5) = 18 - q$

Simplify by adding zeros.

$2 (2 q + 1.5) = 18 - q$

Apply the distributive property.

$2 (2 q) + 2 \cdot 1.5 = 18 - q$

Multiply.

Multiply $2$ by $2$ .

$4 q + 2 \cdot 1.5 = 18 - q$

Multiply $2$ by $1.5$ .

$4 q + 3 = 18 - q$

Step 2

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

Add $q$ to both sides of the equation.

$4 q + 3 + q = 18$

Add $4 q$ and $q$ .

$5 q + 3 = 18$

Step 3

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

Subtract $3$ from both sides of the equation.

$5 q = 18 - 3$

Subtract $3$ from $18$ .

$5 q = 15$

Step 4

Divide each term in $5 q = 15$ by $5$ and simplify.

Divide each term in $5 q = 15$ by $5$ .

$\frac{5 q}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 q}{5} = \frac{15}{5}$

Divide $q$ by $1$ .

$q = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$q = 3$