y^5-8y^4+4y^3=0

Solution for y^5-8y^4+4y^3=0 equation:

Simplifying
y5 + -8y4 + 4y3 = 0

Reorder the terms:
4y3 + -8y4 + y5 = 0

Solving
4y3 + -8y4 + y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y3'.
y3(4 + -8y + y2) = 0

Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 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 '(4 + -8y + y2)' equal to zero and attempt to solve:

Simplifying
4 + -8y + y2 = 0

Solving
4 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + -8y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8y + y2 = 0 + -4
-8y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8y + y2 = -4

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -4 + 16

Reorder the terms:
16 + -8y + y2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8y + y2 = 12

Factor a perfect square on the left side:
(y + -4)(y + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y + -4) equal to 3.464101615 and -3.464101615.

Subproblem 1
y + -4 = 3.464101615

Simplifying
y + -4 = 3.464101615

Reorder the terms:
-4 + y = 3.464101615

Solving
-4 + y = 3.464101615

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + y = 3.464101615 + 4
y = 3.464101615 + 4

Combine like terms: 3.464101615 + 4 = 7.464101615
y = 7.464101615

Simplifying
y = 7.464101615

Subproblem 2
y + -4 = -3.464101615

Simplifying
y + -4 = -3.464101615

Reorder the terms:
-4 + y = -3.464101615

Solving
-4 + y = -3.464101615

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + y = -3.464101615 + 4
y = -3.464101615 + 4

Combine like terms: -3.464101615 + 4 = 0.535898385
y = 0.535898385

Simplifying
y = 0.535898385

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.464101615, 0.535898385}
Solution
y = {7.464101615, 0.535898385}