Solution - Absolute value equations

$$\left(4x-60\right)=-8x+36$$

Add $$$$ to both sides:

$$\left(4x-60\right)+8x=\left(-8x+36\right)+8x$$

Group like terms:

$$\left(4x+8x\right)-60=\left(-8x+36\right)+8x$$

Simplify the arithmetic:

$$12x-60=\left(-8x+36\right)+8x$$

Group like terms:

$$12x-60=\left(-8x+8x\right)+36$$

Simplify the arithmetic:

$$12x-60=36$$

Add $$$$ to both sides:

$$\left(12x-60\right)+60=36+60$$

Simplify the arithmetic:

$$12x=36+60$$

Simplify the arithmetic:

$$12x=96$$

Divide both sides by :

$$\frac{\left(12x\right)}{12}=\frac{96}{12}$$

Simplify the fraction:

$$x=\frac{96}{12}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(8·12\right)}{\left(1·12\right)}$$

Factor out and cancel the greatest common factor:

$$x=8$$

$$\left(4x-60\right)=8x-36$$

Subtract $$$$ from both sides:

$$\left(4x-60\right)-8x=\left(8x-36\right)-8x$$

Group like terms:

$$\left(4x-8x\right)-60=\left(8x-36\right)-8x$$

Simplify the arithmetic:

$$-4x-60=\left(8x-36\right)-8x$$

Group like terms:

$$-4x-60=\left(8x-8x\right)-36$$

Simplify the arithmetic:

$$-4x-60=-36$$

Add $$$$ to both sides:

$$\left(-4x-60\right)+60=-36+60$$

Simplify the arithmetic:

$$-4x=-36+60$$

Simplify the arithmetic:

$$-4x=24$$

Divide both sides by :

$$\frac{\left(-4x\right)}{-4}=\frac{24}{-4}$$

Cancel out the negatives:

$$\frac{4x}{4}=\frac{24}{-4}$$

Simplify the fraction:

$$x=\frac{24}{-4}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-24}{4}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-6·4\right)}{\left(1·4\right)}$$

Factor out and cancel the greatest common factor:

$$x=-6$$