Solve for x 4(x-2)=8(x-3)-12

$4 (x - 2) = 8 (x - 3) - 12$

Step 1

Simplify $4 (x - 2)$ .

Rewrite.

$0 + 0 + 4 (x - 2) = 8 (x - 3) - 12$

Simplify by adding zeros.

$4 (x - 2) = 8 (x - 3) - 12$

Apply the distributive property.

$4 x + 4 \cdot - 2 = 8 (x - 3) - 12$

Multiply $4$ by $- 2$ .

$4 x - 8 = 8 (x - 3) - 12$

Step 2

Simplify $8 (x - 3) - 12$ .

Simplify each term.

Apply the distributive property.

$4 x - 8 = 8 x + 8 \cdot - 3 - 12$

Multiply $8$ by $- 3$ .

$4 x - 8 = 8 x - 24 - 12$

Subtract $12$ from $- 24$ .

$4 x - 8 = 8 x - 36$

Step 3

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

Subtract $8 x$ from both sides of the equation.

$4 x - 8 - 8 x = - 36$

Subtract $8 x$ from $4 x$ .

$- 4 x - 8 = - 36$

Step 4

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

Add $8$ to both sides of the equation.

$- 4 x = - 36 + 8$

Add $- 36$ and $8$ .

$- 4 x = - 28$

Step 5

Divide each term in $- 4 x = - 28$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 28$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 28}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 28}{- 4}$

Simplify the right side.

Divide $- 28$ by $- 4$ .

$x = 7$