0=-20x^2+32x-6

Solution for 0=-20x^2+32x-6 equation:

Simplifying
0 = -20x2 + 32x + -6

Reorder the terms:
0 = -6 + 32x + -20x2

Solving
0 = -6 + 32x + -20x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -32x + 20x2 = -6 + 32x + -20x2 + 6 + -32x + 20x2

Reorder the terms:
6 + -32x + 20x2 = -6 + 6 + 32x + -32x + -20x2 + 20x2

Combine like terms: -6 + 6 = 0
6 + -32x + 20x2 = 0 + 32x + -32x + -20x2 + 20x2
6 + -32x + 20x2 = 32x + -32x + -20x2 + 20x2

Combine like terms: 32x + -32x = 0
6 + -32x + 20x2 = 0 + -20x2 + 20x2
6 + -32x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
6 + -32x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -16x + 10x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -16x + 10x2)' equal to zero and attempt to solve:

Simplifying
3 + -16x + 10x2 = 0

Solving
3 + -16x + 10x2 = 0

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

Divide each side by '10'.
0.3 + -1.6x + x2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + -1.6x + -0.3 + x2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + -1.6x + x2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -1.6x + x2 = 0.0 + -0.3
-1.6x + x2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
-1.6x + x2 = -0.3

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = -0.3 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = -0.3 + 0.64

Combine like terms: -0.3 + 0.64 = 0.34
0.64 + -1.6x + x2 = 0.34

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 0.34

Calculate the square root of the right side: 0.583095189

Break this problem into two subproblems by setting 
(x + -0.8) equal to 0.583095189 and -0.583095189.

Subproblem 1
x + -0.8 = 0.583095189

Simplifying
x + -0.8 = 0.583095189

Reorder the terms:
-0.8 + x = 0.583095189

Solving
-0.8 + x = 0.583095189

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 0.583095189 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 0.583095189 + 0.8
x = 0.583095189 + 0.8

Combine like terms: 0.583095189 + 0.8 = 1.383095189
x = 1.383095189

Simplifying
x = 1.383095189

Subproblem 2
x + -0.8 = -0.583095189

Simplifying
x + -0.8 = -0.583095189

Reorder the terms:
-0.8 + x = -0.583095189

Solving
-0.8 + x = -0.583095189

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -0.583095189 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -0.583095189 + 0.8
x = -0.583095189 + 0.8

Combine like terms: -0.583095189 + 0.8 = 0.216904811
x = 0.216904811

Simplifying
x = 0.216904811

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.383095189, 0.216904811}
Solution
x = {1.383095189, 0.216904811}