-6x+72=6x^2

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

Simplifying
-6x + 72 = 6x2

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

Solving
72 + -6x = 6x2

Solving for variable 'x'.

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

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

Factor a trinomial.
6((3 + -1x)(4 + x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

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