18x=6x^2-108

Solution for 18x=6x^2-108 equation:

Simplifying
18x = 6x2 + -108

Reorder the terms:
18x = -108 + 6x2

Solving
18x = -108 + 6x2

Solving for variable 'x'.

Reorder the terms:
108 + 18x + -6x2 = -108 + 6x2 + 108 + -6x2

Reorder the terms:
108 + 18x + -6x2 = -108 + 108 + 6x2 + -6x2

Combine like terms: -108 + 108 = 0
108 + 18x + -6x2 = 0 + 6x2 + -6x2
108 + 18x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
108 + 18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + 3x + -1x2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {6, -3}