-33x^2+138x-135=0

Solution for -33x^2+138x-135=0 equation:

Simplifying
-33x2 + 138x + -135 = 0

Reorder the terms:
-135 + 138x + -33x2 = 0

Solving
-135 + 138x + -33x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + 46x + -11x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-45 + 46x + -11x2)' equal to zero and attempt to solve:

Simplifying
-45 + 46x + -11x2 = 0

Solving
-45 + 46x + -11x2 = 0

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

Divide each side by '-11'.
4.090909091 + -4.181818182x + x2 = 0

Move the constant term to the right:

Add '-4.090909091' to each side of the equation.
4.090909091 + -4.181818182x + -4.090909091 + x2 = 0 + -4.090909091

Reorder the terms:
4.090909091 + -4.090909091 + -4.181818182x + x2 = 0 + -4.090909091

Combine like terms: 4.090909091 + -4.090909091 = 0.000000000
0.000000000 + -4.181818182x + x2 = 0 + -4.090909091
-4.181818182x + x2 = 0 + -4.090909091

Combine like terms: 0 + -4.090909091 = -4.090909091
-4.181818182x + x2 = -4.090909091

The x term is -4.181818182x.  Take half its coefficient (-2.090909091).
Square it (4.371900827) and add it to both sides.

Add '4.371900827' to each side of the equation.
-4.181818182x + 4.371900827 + x2 = -4.090909091 + 4.371900827

Reorder the terms:
4.371900827 + -4.181818182x + x2 = -4.090909091 + 4.371900827

Combine like terms: -4.090909091 + 4.371900827 = 0.280991736
4.371900827 + -4.181818182x + x2 = 0.280991736

Factor a perfect square on the left side:
(x + -2.090909091)(x + -2.090909091) = 0.280991736

Calculate the square root of the right side: 0.530086536

Break this problem into two subproblems by setting 
(x + -2.090909091) equal to 0.530086536 and -0.530086536.

Subproblem 1
x + -2.090909091 = 0.530086536

Simplifying
x + -2.090909091 = 0.530086536

Reorder the terms:
-2.090909091 + x = 0.530086536

Solving
-2.090909091 + x = 0.530086536

Solving for variable 'x'.

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

Add '2.090909091' to each side of the equation.
-2.090909091 + 2.090909091 + x = 0.530086536 + 2.090909091

Combine like terms: -2.090909091 + 2.090909091 = 0.000000000
0.000000000 + x = 0.530086536 + 2.090909091
x = 0.530086536 + 2.090909091

Combine like terms: 0.530086536 + 2.090909091 = 2.620995627
x = 2.620995627

Simplifying
x = 2.620995627

Subproblem 2
x + -2.090909091 = -0.530086536

Simplifying
x + -2.090909091 = -0.530086536

Reorder the terms:
-2.090909091 + x = -0.530086536

Solving
-2.090909091 + x = -0.530086536

Solving for variable 'x'.

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

Add '2.090909091' to each side of the equation.
-2.090909091 + 2.090909091 + x = -0.530086536 + 2.090909091

Combine like terms: -2.090909091 + 2.090909091 = 0.000000000
0.000000000 + x = -0.530086536 + 2.090909091
x = -0.530086536 + 2.090909091

Combine like terms: -0.530086536 + 2.090909091 = 1.560822555
x = 1.560822555

Simplifying
x = 1.560822555

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.620995627, 1.560822555}
Solution
x = {2.620995627, 1.560822555}