12x^2+45x+27=0

Solution for 12x^2+45x+27=0 equation:

Simplifying
12x2 + 45x + 27 = 0

Reorder the terms:
27 + 45x + 12x2 = 0

Solving
27 + 45x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 15x + 4x2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-3, -0.75}