108=2x^2-6x

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

Simplifying
108 = 2x2 + -6x

Reorder the terms:
108 = -6x + 2x2

Solving
108 = -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
108 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
108 + 6x + -2x2 = 0 + 2x2 + -2x2
108 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
108 + 6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(54 + 3x + -1x2) = 0

Factor a trinomial.
2((9 + -1x)(6 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
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
Solution
x = {9, -6}