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

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

Simplify $3 (x - 4) + 2 x$ .

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 4$ .

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

Add $3 x$ and $2 x$ .

$5 x - 12 = 4 (x - 3) - x$

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

Simplify each term.

Apply the distributive property.

$5 x - 12 = 4 x + 4 \cdot - 3 - x$

Multiply $4$ by $- 3$ .

$5 x - 12 = 4 x - 12 - x$

Subtract $x$ from $4 x$ .

$5 x - 12 = 3 x - 12$

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

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

$5 x - 12 - 3 x = - 12$

Subtract $3 x$ from $5 x$ .

$2 x - 12 = - 12$

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

Add $12$ to both sides of the equation.

$2 x = - 12 + 12$

Add $- 12$ and $12$ .

$2 x = 0$

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 $2$ .

$x = 0$