Solve for x 6x-4(x+1)=4(x-3)+8

$6 x - 4 (x + 1) = 4 (x - 3) + 8$

Step 1

Simplify $6 x - 4 (x + 1)$ .

Simplify each term.

Apply the distributive property.

$6 x - 4 x - 4 \cdot 1 = 4 (x - 3) + 8$

Multiply $- 4$ by $1$ .

$6 x - 4 x - 4 = 4 (x - 3) + 8$

Subtract $4 x$ from $6 x$ .

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

Step 2

Simplify $4 (x - 3) + 8$ .

Simplify each term.

Apply the distributive property.

$2 x - 4 = 4 x + 4 \cdot - 3 + 8$

Multiply $4$ by $- 3$ .

$2 x - 4 = 4 x - 12 + 8$

Add $- 12$ and $8$ .

$2 x - 4 = 4 x - 4$

Step 3

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

Subtract $4 x$ from both sides of the equation.

$2 x - 4 - 4 x = - 4$

Subtract $4 x$ from $2 x$ .

$- 2 x - 4 = - 4$

Step 4

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

Add $4$ to both sides of the equation.

$- 2 x = - 4 + 4$

Add $- 4$ and $4$ .

$- 2 x = 0$

Step 5

Divide each term in $- 2 x = 0$ by $- 2$ and simplify.

Divide each term in $- 2 x = 0$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{0}{- 2}$

Divide $x$ by $1$ .

$x = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$x = 0$