6x^2-6x=72

Solution for 6x^2-6x=72 equation:

Simplifying
6x2 + -6x = 72

Reorder the terms:
-6x + 6x2 = 72

Solving
-6x + 6x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + -6x + 6x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -6x + 6x2 = 0

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

Factor a trinomial.
6((-3 + -1x)(4 + -1x)) = 0

Ignore the factor 6.
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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}