12x^2+36x=-27

Solution for 12x^2+36x=-27 equation:

Simplifying
12x2 + 36x = -27

Reorder the terms:
36x + 12x2 = -27

Solving
36x + 12x2 = -27

Solving for variable 'x'.

Reorder the terms:
27 + 36x + 12x2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 12x + 4x2) = 0

Factor a trinomial.
3((3 + 2x)(3 + 2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-1.5, -1.5}