Solution - Absolute value equations

$$\left(-5x+12\right)-3x=\left(3x-12\right)-3x$$

Group like terms:

$$\left(-5x-3x\right)+12=\left(3x-12\right)-3x$$

Simplify the arithmetic:

$$-8x+12=\left(3x-12\right)-3x$$

Group like terms:

$$-8x+12=\left(3x-3x\right)-12$$

Simplify the arithmetic:

$$-8x+12=-12$$

Subtract $$$$ from both sides:

$$\left(-8x+12\right)-12=-12-12$$

Simplify the arithmetic:

$$-8x=-12-12$$

Simplify the arithmetic:

$$-8x=-24$$

Divide both sides by :

$$\frac{\left(-8x\right)}{-8}=\frac{-24}{-8}$$

Cancel out the negatives:

$$\frac{8x}{8}=\frac{-24}{-8}$$

Simplify the fraction:

$$x=\frac{-24}{-8}$$

Cancel out the negatives:

$$x=\frac{24}{8}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(3·8\right)}{\left(1·8\right)}$$

Factor out and cancel the greatest common factor:

$$x=3$$

$$\left(-5x+12\right)=-3x+12$$

Add $$$$ to both sides:

$$\left(-5x+12\right)+3x=\left(-3x+12\right)+3x$$

Group like terms:

$$\left(-5x+3x\right)+12=\left(-3x+12\right)+3x$$

Simplify the arithmetic:

$$-2x+12=\left(-3x+12\right)+3x$$

Group like terms:

$$-2x+12=\left(-3x+3x\right)+12$$

Simplify the arithmetic:

$$-2x+12=12$$

Subtract $$$$ from both sides:

$$\left(-2x+12\right)-12=12-12$$

Simplify the arithmetic:

$$-2x=12-12$$

Simplify the arithmetic:

$$-2x=0$$

Divide both sides by the coefficient:

$$x=0$$