x^2+42x+117=0

Solution for x^2+42x+117=0 equation:

Simplifying
x2 + 42x + 117 = 0

Reorder the terms:
117 + 42x + x2 = 0

Solving
117 + 42x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(39 + x)(3 + x) = 0

Subproblem 1
Set the factor '(39 + x)' equal to zero and attempt to solve:

Simplifying
39 + x = 0

Solving
39 + x = 0

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

Add '-39' to each side of the equation.
39 + -39 + x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + x = 0 + -39
x = 0 + -39

Combine like terms: 0 + -39 = -39
x = -39

Simplifying
x = -39
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-39, -3}