-3x^2+36x=108

Solution for -3x^2+36x=108 equation:

Simplifying
-3x2 + 36x = 108

Reorder the terms:
36x + -3x2 = 108

Solving
36x + -3x2 = 108

Solving for variable 'x'.

Reorder the terms:
-108 + 36x + -3x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 36x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + 12x + -1x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

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

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6, 6}