Solve for x 2x+3(x-2)=6(x+1)+x

$2 x + 3 (x - 2) = 6 (x + 1) + x$

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

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

$2 x + 3 x - 6 = 6 (x + 1) + x$

Add $2 x$ and $3 x$ .

$5 x - 6 = 6 (x + 1) + x$

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

Simplify each term.

Apply the distributive property.

$5 x - 6 = 6 x + 6 \cdot 1 + x$

Multiply $6$ by $1$ .

$5 x - 6 = 6 x + 6 + x$

Add $6 x$ and $x$ .

$5 x - 6 = 7 x + 6$

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

Subtract $7 x$ from both sides of the equation.

$5 x - 6 - 7 x = 6$

Subtract $7 x$ from $5 x$ .

$- 2 x - 6 = 6$

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

Add $6$ to both sides of the equation.

$- 2 x = 6 + 6$

Add $6$ and $6$ .

$- 2 x = 12$

Divide each term in $- 2 x = 12$ by $- 2$ and simplify.

Divide each term in $- 2 x = 12$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Divide $x$ by $1$ .

$x = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x = - 6$