2x^2+54x+12=0

Solution for 2x^2+54x+12=0 equation:

Simplifying
2x2 + 54x + 12 = 0

Reorder the terms:
12 + 54x + 2x2 = 0

Solving
12 + 54x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 27x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 27x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 27x + x2 = 0

Solving
6 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 27x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 27x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 27x + x2 = 0 + -6
27x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
27x + x2 = -6

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = -6 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -6 + 182.25

Combine like terms: -6 + 182.25 = 176.25
182.25 + 27x + x2 = 176.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 176.25

Calculate the square root of the right side: 13.275918047

Break this problem into two subproblems by setting 
(x + 13.5) equal to 13.275918047 and -13.275918047.

Subproblem 1
x + 13.5 = 13.275918047

Simplifying
x + 13.5 = 13.275918047

Reorder the terms:
13.5 + x = 13.275918047

Solving
13.5 + x = 13.275918047

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 13.275918047 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 13.275918047 + -13.5
x = 13.275918047 + -13.5

Combine like terms: 13.275918047 + -13.5 = -0.224081953
x = -0.224081953

Simplifying
x = -0.224081953

Subproblem 2
x + 13.5 = -13.275918047

Simplifying
x + 13.5 = -13.275918047

Reorder the terms:
13.5 + x = -13.275918047

Solving
13.5 + x = -13.275918047

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -13.275918047 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -13.275918047 + -13.5
x = -13.275918047 + -13.5

Combine like terms: -13.275918047 + -13.5 = -26.775918047
x = -26.775918047

Simplifying
x = -26.775918047

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.224081953, -26.775918047}
Solution
x = {-0.224081953, -26.775918047}