3x^2+39x=-108

Solution for 3x^2+39x=-108 equation:

Simplifying
3x2 + 39x = -108

Reorder the terms:
39x + 3x2 = -108

Solving
39x + 3x2 = -108

Solving for variable 'x'.

Reorder the terms:
108 + 39x + 3x2 = -108 + 108

Combine like terms: -108 + 108 = 0
108 + 39x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + 13x + x2) = 0

Factor a trinomial.
3((9 + x)(4 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
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 = {-9, -4}