-150x^2+165x-20=0

Solution for -150x^2+165x-20=0 equation:

Simplifying
-150x2 + 165x + -20 = 0

Reorder the terms:
-20 + 165x + -150x2 = 0

Solving
-20 + 165x + -150x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 33x + -30x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + 33x + -30x2)' equal to zero and attempt to solve:

Simplifying
-4 + 33x + -30x2 = 0

Solving
-4 + 33x + -30x2 = 0

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
0.1333333333 + -1.1x + x2 = 0.0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -1.1x + -0.1333333333 + x2 = 0.0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -1.1x + x2 = 0.0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -1.1x + x2 = 0.0 + -0.1333333333
-1.1x + x2 = 0.0 + -0.1333333333

Combine like terms: 0.0 + -0.1333333333 = -0.1333333333
-1.1x + x2 = -0.1333333333

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = -0.1333333333 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = -0.1333333333 + 0.3025

Combine like terms: -0.1333333333 + 0.3025 = 0.1691666667
0.3025 + -1.1x + x2 = 0.1691666667

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 0.1691666667

Calculate the square root of the right side: 0.411298756

Break this problem into two subproblems by setting 
(x + -0.55) equal to 0.411298756 and -0.411298756.

Subproblem 1
x + -0.55 = 0.411298756

Simplifying
x + -0.55 = 0.411298756

Reorder the terms:
-0.55 + x = 0.411298756

Solving
-0.55 + x = 0.411298756

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 0.411298756 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 0.411298756 + 0.55
x = 0.411298756 + 0.55

Combine like terms: 0.411298756 + 0.55 = 0.961298756
x = 0.961298756

Simplifying
x = 0.961298756

Subproblem 2
x + -0.55 = -0.411298756

Simplifying
x + -0.55 = -0.411298756

Reorder the terms:
-0.55 + x = -0.411298756

Solving
-0.55 + x = -0.411298756

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -0.411298756 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -0.411298756 + 0.55
x = -0.411298756 + 0.55

Combine like terms: -0.411298756 + 0.55 = 0.138701244
x = 0.138701244

Simplifying
x = 0.138701244

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.961298756, 0.138701244}
Solution
x = {0.961298756, 0.138701244}