27x^2+108x+108=0

Solution for 27x^2+108x+108=0 equation:

Simplifying
27x2 + 108x + 108 = 0

Reorder the terms:
108 + 108x + 27x2 = 0

Solving
108 + 108x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '27'.
27(4 + 4x + x2) = 0

Factor a trinomial.
27((2 + x)(2 + x)) = 0

Ignore the factor 27.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-2, -2}