0=x^2+26x+120

Solution for 0=x^2+26x+120 equation:

Simplifying
0 = x2 + 26x + 120

Reorder the terms:
0 = 120 + 26x + x2

Solving
0 = 120 + 26x + x2

Solving for variable 'x'.

Combine like terms: 0 + -120 = -120
-120 + -26x + -1x2 = 120 + 26x + x2 + -120 + -26x + -1x2

Reorder the terms:
-120 + -26x + -1x2 = 120 + -120 + 26x + -26x + x2 + -1x2

Combine like terms: 120 + -120 = 0
-120 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2
-120 + -26x + -1x2 = 26x + -26x + x2 + -1x2

Combine like terms: 26x + -26x = 0
-120 + -26x + -1x2 = 0 + x2 + -1x2
-120 + -26x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-120 + -26x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(120 + 26x + x2) = 0

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

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

Simplifying
20 + x = 0

Solving
20 + x = 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 + x = 0 + -20

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

Combine like terms: 0 + -20 = -20
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}