Solve for g -7g=3g+8(-g+2)

$- 7 g = 3 g + 8 (- g + 2)$

Step 1

Since $g$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 g + 8 (- g + 2) = - 7 g$

Step 2

Simplify $3 g + 8 (- g + 2)$ .

Simplify each term.

Apply the distributive property.

$3 g + 8 (- g) + 8 \cdot 2 = - 7 g$

Multiply $- 1$ by $8$ .

$3 g - 8 g + 8 \cdot 2 = - 7 g$

Multiply $8$ by $2$ .

$3 g - 8 g + 16 = - 7 g$

Subtract $8 g$ from $3 g$ .

$- 5 g + 16 = - 7 g$

Step 3

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

Add $7 g$ to both sides of the equation.

$- 5 g + 16 + 7 g = 0$

Add $- 5 g$ and $7 g$ .

$2 g + 16 = 0$

Step 4

Subtract $16$ from both sides of the equation.

$2 g = - 16$

Step 5

Divide each term in $2 g = - 16$ by $2$ and simplify.

Divide each term in $2 g = - 16$ by $2$ .

$\frac{2 g}{2} = \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 g}{2} = \frac{- 16}{2}$

Divide $g$ by $1$ .

$g = \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$g = - 8$