0=120+23x+x^2

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Solution for 0=120+23x+x^2 equation: 


Simplifying
0 = 120 + 23x + x2

Solving
0 = 120 + 23x + x2

Solving for variable 'x'.

Combine like terms: 0 + -120 = -120
-120 + -23x + -1x2 = 120 + 23x + x2 + -120 + -23x + -1x2

Reorder the terms:
-120 + -23x + -1x2 = 120 + -120 + 23x + -23x + x2 + -1x2

Combine like terms: 120 + -120 = 0
-120 + -23x + -1x2 = 0 + 23x + -23x + x2 + -1x2
-120 + -23x + -1x2 = 23x + -23x + x2 + -1x2

Combine like terms: 23x + -23x = 0
-120 + -23x + -1x2 = 0 + x2 + -1x2
-120 + -23x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-120 + -23x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(120 + 23x + x2) = 0

Factor a trinomial.
-1((15 + x)(8 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-15, -8}

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