0=2x^2-14x-120

Solution for 0=2x^2-14x-120 equation:

Simplifying
0 = 2x2 + -14x + -120

Reorder the terms:
0 = -120 + -14x + 2x2

Solving
0 = -120 + -14x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 120 = 120
120 + 14x + -2x2 = -120 + -14x + 2x2 + 120 + 14x + -2x2

Reorder the terms:
120 + 14x + -2x2 = -120 + 120 + -14x + 14x + 2x2 + -2x2

Combine like terms: -120 + 120 = 0
120 + 14x + -2x2 = 0 + -14x + 14x + 2x2 + -2x2
120 + 14x + -2x2 = -14x + 14x + 2x2 + -2x2

Combine like terms: -14x + 14x = 0
120 + 14x + -2x2 = 0 + 2x2 + -2x2
120 + 14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
120 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + 7x + -1x2) = 0

Factor a trinomial.
2((12 + -1x)(5 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {12, -5}