0=x^2-23x-108

Solution for 0=x^2-23x-108 equation:

Simplifying
0 = x2 + -23x + -108

Reorder the terms:
0 = -108 + -23x + x2

Solving
0 = -108 + -23x + x2

Solving for variable 'x'.

Combine like terms: 0 + 108 = 108
108 + 23x + -1x2 = -108 + -23x + x2 + 108 + 23x + -1x2

Reorder the terms:
108 + 23x + -1x2 = -108 + 108 + -23x + 23x + x2 + -1x2

Combine like terms: -108 + 108 = 0
108 + 23x + -1x2 = 0 + -23x + 23x + x2 + -1x2
108 + 23x + -1x2 = -23x + 23x + x2 + -1x2

Combine like terms: -23x + 23x = 0
108 + 23x + -1x2 = 0 + x2 + -1x2
108 + 23x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
108 + 23x + -1x2 = 0

Factor a trinomial.
(27 + -1x)(4 + x) = 0

Subproblem 1
Set the factor '(27 + -1x)' equal to zero and attempt to solve:

Simplifying
27 + -1x = 0

Solving
27 + -1x = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1x = 0 + -27
-1x = 0 + -27

Combine like terms: 0 + -27 = -27
-1x = -27

Divide each side by '-1'.
x = 27

Simplifying
x = 27
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {27, -4}