x^2+31x+108=0

Solution for x^2+31x+108=0 equation:

Simplifying
x2 + 31x + 108 = 0

Reorder the terms:
108 + 31x + x2 = 0

Solving
108 + 31x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
27 + x = 0

Solving
27 + x = 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 + x = 0 + -27

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

Combine like terms: 0 + -27 = -27
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}