2x^2-8x=120

Solution for 2x^2-8x=120 equation:

Simplifying
2x2 + -8x = 120

Reorder the terms:
-8x + 2x2 = 120

Solving
-8x + 2x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + -8x + 2x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -4x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-6, 10}