Solve for x 3(x-4)=2x-(6+x)

$3 (x - 4) = 2 x - (6 + x)$

Step 1

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

$2 x - (6 + x) = 3 (x - 4)$

Step 2

Simplify $2 x - (6 + x)$ .

Simplify each term.

Apply the distributive property.

$2 x - 1 \cdot 6 - x = 3 (x - 4)$

Multiply $- 1$ by $6$ .

$2 x - 6 - x = 3 (x - 4)$

Subtract $x$ from $2 x$ .

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

Step 3

Simplify $3 (x - 4)$ .

Apply the distributive property.

$x - 6 = 3 x + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$x - 6 = 3 x - 12$

Step 4

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

Subtract $3 x$ from both sides of the equation.

$x - 6 - 3 x = - 12$

Subtract $3 x$ from $x$ .

$- 2 x - 6 = - 12$

Step 5

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

Add $6$ to both sides of the equation.

$- 2 x = - 12 + 6$

Add $- 12$ and $6$ .

$- 2 x = - 6$

Step 6

Divide each term in $- 2 x = - 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 2}$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$x = 3$