12x^2+324x-9000=0

Solution for 12x^2+324x-9000=0 equation:

Simplifying
12x2 + 324x + -9000 = 0

Reorder the terms:
-9000 + 324x + 12x2 = 0

Solving
-9000 + 324x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-750 + 27x + x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-750 + 27x + x2)' equal to zero and attempt to solve:

Simplifying
-750 + 27x + x2 = 0

Solving
-750 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '750' to each side of the equation.
-750 + 27x + 750 + x2 = 0 + 750

Reorder the terms:
-750 + 750 + 27x + x2 = 0 + 750

Combine like terms: -750 + 750 = 0
0 + 27x + x2 = 0 + 750
27x + x2 = 0 + 750

Combine like terms: 0 + 750 = 750
27x + x2 = 750

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 = 750 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 750 + 182.25

Combine like terms: 750 + 182.25 = 932.25
182.25 + 27x + x2 = 932.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 932.25

Calculate the square root of the right side: 30.532769282

Break this problem into two subproblems by setting 
(x + 13.5) equal to 30.532769282 and -30.532769282.

Subproblem 1
x + 13.5 = 30.532769282

Simplifying
x + 13.5 = 30.532769282

Reorder the terms:
13.5 + x = 30.532769282

Solving
13.5 + x = 30.532769282

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 = 30.532769282 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 30.532769282 + -13.5
x = 30.532769282 + -13.5

Combine like terms: 30.532769282 + -13.5 = 17.032769282
x = 17.032769282

Simplifying
x = 17.032769282

Subproblem 2
x + 13.5 = -30.532769282

Simplifying
x + 13.5 = -30.532769282

Reorder the terms:
13.5 + x = -30.532769282

Solving
13.5 + x = -30.532769282

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 = -30.532769282 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -30.532769282 + -13.5
x = -30.532769282 + -13.5

Combine like terms: -30.532769282 + -13.5 = -44.032769282
x = -44.032769282

Simplifying
x = -44.032769282

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.032769282, -44.032769282}
Solution
x = {17.032769282, -44.032769282}