20x^5-40x^4+5x^3=

Solution for 20x^5-40x^4+5x^3= equation:

Simplifying
20x5 + -40x4 + 5x3 = 0

Reorder the terms:
5x3 + -40x4 + 20x5 = 0

Solving
5x3 + -40x4 + 20x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x3'.
5x3(1 + -8x + 4x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -8x + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + -8x + 4x2 = 0

Solving
1 + -8x + 4x2 = 0

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

Divide each side by '4'.
0.25 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2x + x2 = 0 + -0.25
-2x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2x + x2 = -0.25

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.25 + 1

Reorder the terms:
1 + -2x + x2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + -2x + x2 = 0.75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(x + -1) equal to 0.866025404 and -0.866025404.

Subproblem 1
x + -1 = 0.866025404

Simplifying
x + -1 = 0.866025404

Reorder the terms:
-1 + x = 0.866025404

Solving
-1 + x = 0.866025404

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.866025404 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.866025404 + 1
x = 0.866025404 + 1

Combine like terms: 0.866025404 + 1 = 1.866025404
x = 1.866025404

Simplifying
x = 1.866025404

Subproblem 2
x + -1 = -0.866025404

Simplifying
x + -1 = -0.866025404

Reorder the terms:
-1 + x = -0.866025404

Solving
-1 + x = -0.866025404

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.866025404 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.866025404 + 1
x = -0.866025404 + 1

Combine like terms: -0.866025404 + 1 = 0.133974596
x = 0.133974596

Simplifying
x = 0.133974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.866025404, 0.133974596}
Solution
x = {1.866025404, 0.133974596}