Solve for q -13(q+4)=7q+16

$- 13 (q + 4) = 7 q + 16$

Step 1

Simplify $- 13 (q + 4)$ .

Rewrite.

$0 + 0 - 13 (q + 4) = 7 q + 16$

Simplify by adding zeros.

$- 13 (q + 4) = 7 q + 16$

Apply the distributive property.

$- 13 q - 13 \cdot 4 = 7 q + 16$

Multiply $- 13$ by $4$ .

$- 13 q - 52 = 7 q + 16$

Step 2

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

Subtract $7 q$ from both sides of the equation.

$- 13 q - 52 - 7 q = 16$

Subtract $7 q$ from $- 13 q$ .

$- 20 q - 52 = 16$

Step 3

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

Add $52$ to both sides of the equation.

$- 20 q = 16 + 52$

Add $16$ and $52$ .

$- 20 q = 68$

Step 4

Divide each term in $- 20 q = 68$ by $- 20$ and simplify.

Divide each term in $- 20 q = 68$ by $- 20$ .

$\frac{- 20 q}{- 20} = \frac{68}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 q}{- 20} = \frac{68}{- 20}$

Divide $q$ by $1$ .

$q = \frac{68}{- 20}$

Simplify the right side.

Cancel the common factor of $68$ and $- 20$ .

Factor $4$ out of $68$ .

$q = \frac{4 (17)}{- 20}$

Cancel the common factors.

Factor $4$ out of $- 20$ .

$q = \frac{4 \cdot 17}{4 \cdot - 5}$

Cancel the common factor.

$q = \frac{4 \cdot 17}{4 \cdot - 5}$

Rewrite the expression.

$q = \frac{17}{- 5}$

Move the negative in front of the fraction.

$q = - \frac{17}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{17}{5}$

Decimal Form:

$q = - 3.4$

Mixed Number Form:

$q = - 3 \frac{2}{5}$

Solve for q -13(q+4)=7q+16

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