Solve for r -4(r+2)=4(2-2r)

$- 4 (r + 2) = 4 (2 - 2 r)$

Step 1

Simplify $- 4 (r + 2)$ .

Start simplifying.

$0 + 0 - 4 (r + 2) = 4 (2 - 2 r)$

Simplify by adding zeros.

$- 4 (r + 2) = 4 (2 - 2 r)$

Apply the distributive property.

$- 4 r - 4 \cdot 2 = 4 (2 - 2 r)$

Multiply $- 4$ by $2$ .

$- 4 r - 8 = 4 (2 - 2 r)$

Step 2

Simplify $4 (2 - 2 r)$ .

Apply the distributive property.

$- 4 r - 8 = 4 \cdot 2 + 4 (- 2 r)$

Multiply.

Multiply $4$ by $2$ .

$- 4 r - 8 = 8 + 4 (- 2 r)$

Multiply $- 2$ by $4$ .

$- 4 r - 8 = 8 - 8 r$

Step 3

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

Add $8 r$ to both sides of the equation.

$- 4 r - 8 + 8 r = 8$

Add $- 4 r$ and $8 r$ .

$4 r - 8 = 8$

Step 4

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

Add $8$ to both sides of the equation.

$4 r = 8 + 8$

Add $8$ and $8$ .

$4 r = 16$

Step 5

Divide each term in $4 r = 16$ by $4$ and simplify.

Divide each term in $4 r = 16$ by $4$ .

$\frac{4 r}{4} = \frac{16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 r}{4} = \frac{16}{4}$

Divide $r$ by $1$ .

$r = \frac{16}{4}$

Simplify the right side.

Divide $16$ by $4$ .

$r = 4$