# How do you solve -4(-d-4)=-4d+6(2d+6)?

Jan 12, 2017

$d = - 5$

#### Explanation:

The first step is to distribute brackets on both sides of the equation.

$\Rightarrow 4 d + 16 = - 4 d + 12 d + 36$

simplifying right side.

$4 d + 16 = 8 d + 36$

Collect terms in d, on the left side and numeric values on the right.

subtract 8d from both sides.

$4 d - 8 d + 16 = \cancel{8 d} \cancel{- 8 d} + 36$

$\Rightarrow - 4 d + 16 = 36$

subtract 16 from both sides.

$- 4 \mathrm{dc} a n c e l \left(+ 16\right) \cancel{- 16} = 36 - 16$

$\Rightarrow - 4 d = 20$

To solve for d, divide both sides by - 4

$\frac{\cancel{- 4} d}{\cancel{- 4}} = \frac{20}{- 4}$

$\Rightarrow d = - 5$

$\textcolor{b l u e}{\text{As a check}}$

$\text{left side } = - 4 \left(- \left(- 5\right) - 4\right) = - 4 \times 1 = - 4$

$\text{right side } = \left(- 4 \times - 5\right) + 6 \left(2 \times \left(- 5\right) + 6\right)$

$= 20 + 6 \left(- 10 + 6\right) = 20 + 6 \left(- 4\right) = 20 - 24 = - 4$

$\text{Thus both sides } = - 4$

$\Rightarrow d = - 5 \text{ is the solution}$