2x^2-120=22x

Solution for 2x^2-120=22x equation:

Simplifying
2x2 + -120 = 22x

Reorder the terms:
-120 + 2x2 = 22x

Solving
-120 + 2x2 = 22x

Solving for variable 'x'.

Reorder the terms:
-120 + -22x + 2x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
-120 + -22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -11x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(15 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-4, 15}