2x^2=120-8x

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

Simplifying
2x2 = 120 + -8x

Solving
2x2 = 120 + -8x

Solving for variable 'x'.

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

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

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

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

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

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

Ignore the factor 2.
Subproblem 1
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
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 = {-10, 6}