0=x^2-14x-120

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

Simplifying
0 = x2 + -14x + -120

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

Solving
0 = -120 + -14x + x2

Solving for variable 'x'.

Combine like terms: 0 + 120 = 120
120 + 14x + -1x2 = -120 + -14x + x2 + 120 + 14x + -1x2

Reorder the terms:
120 + 14x + -1x2 = -120 + 120 + -14x + 14x + x2 + -1x2

Combine like terms: -120 + 120 = 0
120 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2
120 + 14x + -1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
120 + 14x + -1x2 = 0 + x2 + -1x2
120 + 14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
120 + 14x + -1x2 = 0

Factor a trinomial.
(20 + -1x)(6 + x) = 0

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
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 = {20, -6}