-72*x^2+640*x-160=0

Solution for -72*x^2+640*x-160=0 equation:

Simplifying
-72x2 + 640x + -160 = 0

Reorder the terms:
-160 + 640x + -72x2 = 0

Solving
-160 + 640x + -72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-20 + 80x + -9x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-20 + 80x + -9x2)' equal to zero and attempt to solve:

Simplifying
-20 + 80x + -9x2 = 0

Solving
-20 + 80x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
2.222222222 + -8.888888889x + x2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + -8.888888889x + -2.222222222 + x2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + -8.888888889x + x2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + -8.888888889x + x2 = 0 + -2.222222222
-8.888888889x + x2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
-8.888888889x + x2 = -2.222222222

The x term is -8.888888889x.  Take half its coefficient (-4.444444445).
Square it (19.75308642) and add it to both sides.

Add '19.75308642' to each side of the equation.
-8.888888889x + 19.75308642 + x2 = -2.222222222 + 19.75308642

Reorder the terms:
19.75308642 + -8.888888889x + x2 = -2.222222222 + 19.75308642

Combine like terms: -2.222222222 + 19.75308642 = 17.530864198
19.75308642 + -8.888888889x + x2 = 17.530864198

Factor a perfect square on the left side:
(x + -4.444444445)(x + -4.444444445) = 17.530864198

Calculate the square root of the right side: 4.186987485

Break this problem into two subproblems by setting 
(x + -4.444444445) equal to 4.186987485 and -4.186987485.

Subproblem 1
x + -4.444444445 = 4.186987485

Simplifying
x + -4.444444445 = 4.186987485

Reorder the terms:
-4.444444445 + x = 4.186987485

Solving
-4.444444445 + x = 4.186987485

Solving for variable 'x'.

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

Add '4.444444445' to each side of the equation.
-4.444444445 + 4.444444445 + x = 4.186987485 + 4.444444445

Combine like terms: -4.444444445 + 4.444444445 = 0.000000000
0.000000000 + x = 4.186987485 + 4.444444445
x = 4.186987485 + 4.444444445

Combine like terms: 4.186987485 + 4.444444445 = 8.63143193
x = 8.63143193

Simplifying
x = 8.63143193

Subproblem 2
x + -4.444444445 = -4.186987485

Simplifying
x + -4.444444445 = -4.186987485

Reorder the terms:
-4.444444445 + x = -4.186987485

Solving
-4.444444445 + x = -4.186987485

Solving for variable 'x'.

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

Add '4.444444445' to each side of the equation.
-4.444444445 + 4.444444445 + x = -4.186987485 + 4.444444445

Combine like terms: -4.444444445 + 4.444444445 = 0.000000000
0.000000000 + x = -4.186987485 + 4.444444445
x = -4.186987485 + 4.444444445

Combine like terms: -4.186987485 + 4.444444445 = 0.25745696
x = 0.25745696

Simplifying
x = 0.25745696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.63143193, 0.25745696}
Solution
x = {8.63143193, 0.25745696}