Solution - Absolute value equations

$$\left(3x-3\right)-6x=\left(6x+3\right)-6x$$

Group like terms:

$$\left(3x-6x\right)-3=\left(6x+3\right)-6x$$

Simplify the arithmetic:

$$-3x-3=\left(6x+3\right)-6x$$

Group like terms:

$$-3x-3=\left(6x-6x\right)+3$$

Simplify the arithmetic:

$$-3x-3=3$$

Add $$$$ to both sides:

$$\left(-3x-3\right)+3=3+3$$

Simplify the arithmetic:

$$-3x=3+3$$

Simplify the arithmetic:

$$-3x=6$$

Divide both sides by :

$$\frac{\left(-3x\right)}{-3}=\frac{6}{-3}$$

Cancel out the negatives:

$$\frac{3x}{3}=\frac{6}{-3}$$

Simplify the fraction:

$$x=\frac{6}{-3}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-6}{3}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-2·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$x=-2$$

$$\left(3x-3\right)=-6x-3$$

Add $$$$ to both sides:

$$\left(3x-3\right)+6x=\left(-6x-3\right)+6x$$

Group like terms:

$$\left(3x+6x\right)-3=\left(-6x-3\right)+6x$$

Simplify the arithmetic:

$$9x-3=\left(-6x-3\right)+6x$$

Group like terms:

$$9x-3=\left(-6x+6x\right)-3$$

Simplify the arithmetic:

$$9x-3=-3$$

Add $$$$ to both sides:

$$\left(9x-3\right)+3=-3+3$$

Simplify the arithmetic:

$$9x=-3+3$$

Simplify the arithmetic:

$$9x=0$$

Divide both sides by the coefficient:

$$x=0$$