0=12x^2-12x-72

Solution for 0=12x^2-12x-72 equation:

Simplifying
0 = 12x2 + -12x + -72

Reorder the terms:
0 = -72 + -12x + 12x2

Solving
0 = -72 + -12x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 72 = 72
72 + 12x + -12x2 = -72 + -12x + 12x2 + 72 + 12x + -12x2

Reorder the terms:
72 + 12x + -12x2 = -72 + 72 + -12x + 12x + 12x2 + -12x2

Combine like terms: -72 + 72 = 0
72 + 12x + -12x2 = 0 + -12x + 12x + 12x2 + -12x2
72 + 12x + -12x2 = -12x + 12x + 12x2 + -12x2

Combine like terms: -12x + 12x = 0
72 + 12x + -12x2 = 0 + 12x2 + -12x2
72 + 12x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
72 + 12x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(6 + x + -1x2) = 0

Factor a trinomial.
12((3 + -1x)(2 + x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {3, -2}