33x^2-360x-2700=0

Solution for 33x^2-360x-2700=0 equation:

Simplifying
33x2 + -360x + -2700 = 0

Reorder the terms:
-2700 + -360x + 33x2 = 0

Solving
-2700 + -360x + 33x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-900 + -120x + 11x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-900 + -120x + 11x2)' equal to zero and attempt to solve:

Simplifying
-900 + -120x + 11x2 = 0

Solving
-900 + -120x + 11x2 = 0

Begin completing the square.  Divide all terms by
11 the coefficient of the squared term: 

Divide each side by '11'.
-81.81818182 + -10.90909091x + x2 = 0

Move the constant term to the right:

Add '81.81818182' to each side of the equation.
-81.81818182 + -10.90909091x + 81.81818182 + x2 = 0 + 81.81818182

Reorder the terms:
-81.81818182 + 81.81818182 + -10.90909091x + x2 = 0 + 81.81818182

Combine like terms: -81.81818182 + 81.81818182 = 0.00000000
0.00000000 + -10.90909091x + x2 = 0 + 81.81818182
-10.90909091x + x2 = 0 + 81.81818182

Combine like terms: 0 + 81.81818182 = 81.81818182
-10.90909091x + x2 = 81.81818182

The x term is -10.90909091x.  Take half its coefficient (-5.454545455).
Square it (29.75206612) and add it to both sides.

Add '29.75206612' to each side of the equation.
-10.90909091x + 29.75206612 + x2 = 81.81818182 + 29.75206612

Reorder the terms:
29.75206612 + -10.90909091x + x2 = 81.81818182 + 29.75206612

Combine like terms: 81.81818182 + 29.75206612 = 111.57024794
29.75206612 + -10.90909091x + x2 = 111.57024794

Factor a perfect square on the left side:
(x + -5.454545455)(x + -5.454545455) = 111.57024794

Calculate the square root of the right side: 10.562681854

Break this problem into two subproblems by setting 
(x + -5.454545455) equal to 10.562681854 and -10.562681854.

Subproblem 1
x + -5.454545455 = 10.562681854

Simplifying
x + -5.454545455 = 10.562681854

Reorder the terms:
-5.454545455 + x = 10.562681854

Solving
-5.454545455 + x = 10.562681854

Solving for variable 'x'.

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

Add '5.454545455' to each side of the equation.
-5.454545455 + 5.454545455 + x = 10.562681854 + 5.454545455

Combine like terms: -5.454545455 + 5.454545455 = 0.000000000
0.000000000 + x = 10.562681854 + 5.454545455
x = 10.562681854 + 5.454545455

Combine like terms: 10.562681854 + 5.454545455 = 16.017227309
x = 16.017227309

Simplifying
x = 16.017227309

Subproblem 2
x + -5.454545455 = -10.562681854

Simplifying
x + -5.454545455 = -10.562681854

Reorder the terms:
-5.454545455 + x = -10.562681854

Solving
-5.454545455 + x = -10.562681854

Solving for variable 'x'.

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

Add '5.454545455' to each side of the equation.
-5.454545455 + 5.454545455 + x = -10.562681854 + 5.454545455

Combine like terms: -5.454545455 + 5.454545455 = 0.000000000
0.000000000 + x = -10.562681854 + 5.454545455
x = -10.562681854 + 5.454545455

Combine like terms: -10.562681854 + 5.454545455 = -5.108136399
x = -5.108136399

Simplifying
x = -5.108136399

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.017227309, -5.108136399}
Solution
x = {16.017227309, -5.108136399}