Solve for r -6(2r+8)=-10(r-3)

$- 6 (2 r + 8) = - 10 (r - 3)$

Step 1

Simplify $- 6 (2 r + 8)$ .

Start simplifying.

$0 + 0 - 6 (2 r + 8) = - 10 (r - 3)$

Simplify by adding zeros.

$- 6 (2 r + 8) = - 10 (r - 3)$

Apply the distributive property.

$- 6 (2 r) - 6 \cdot 8 = - 10 (r - 3)$

Multiply.

Multiply $2$ by $- 6$ .

$- 12 r - 6 \cdot 8 = - 10 (r - 3)$

Multiply $- 6$ by $8$ .

$- 12 r - 48 = - 10 (r - 3)$

Step 2

Simplify $- 10 (r - 3)$ .

Apply the distributive property.

$- 12 r - 48 = - 10 r - 10 \cdot - 3$

Multiply $- 10$ by $- 3$ .

$- 12 r - 48 = - 10 r + 30$

Step 3

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

Add $10 r$ to both sides of the equation.

$- 12 r - 48 + 10 r = 30$

Add $- 12 r$ and $10 r$ .

$- 2 r - 48 = 30$

Step 4

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

Add $48$ to both sides of the equation.

$- 2 r = 30 + 48$

Add $30$ and $48$ .

$- 2 r = 78$

Step 5

Divide each term in $- 2 r = 78$ by $- 2$ and simplify.

Divide each term in $- 2 r = 78$ by $- 2$ .

$\frac{- 2 r}{- 2} = \frac{78}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 r}{- 2} = \frac{78}{- 2}$

Divide $r$ by $1$ .

$r = \frac{78}{- 2}$

Simplify the right side.

Divide $78$ by $- 2$ .

$r = - 39$