Solve for x 6(2x-3)-3x=2x-18+x

$6 (2 x - 3) - 3 x = 2 x - 18 + x$

Step 1

Simplify $6 (2 x - 3) - 3 x$ .

Simplify each term.

Apply the distributive property.

$6 (2 x) + 6 \cdot - 3 - 3 x = 2 x - 18 + x$

Multiply $2$ by $6$ .

$12 x + 6 \cdot - 3 - 3 x = 2 x - 18 + x$

Multiply $6$ by $- 3$ .

$12 x - 18 - 3 x = 2 x - 18 + x$

Subtract $3 x$ from $12 x$ .

$9 x - 18 = 2 x - 18 + x$

Step 2

Add $2 x$ and $x$ .

$9 x - 18 = 3 x - 18$

Step 3

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

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

$9 x - 18 - 3 x = - 18$

Subtract $3 x$ from $9 x$ .

$6 x - 18 = - 18$

Step 4

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

Add $18$ to both sides of the equation.

$6 x = - 18 + 18$

Add $- 18$ and $18$ .

$6 x = 0$

Step 5

Divide each term in $6 x = 0$ by $6$ and simplify.

Divide each term in $6 x = 0$ by $6$ .

$\frac{6 x}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{0}{6}$

Divide $x$ by $1$ .

$x = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

$x = 0$