5y^5(y^2-8y+6)=

Solution for 5y^5(y^2-8y+6)= equation:

Simplifying
5y5(y2 + -8y + 6) = 0

Reorder the terms:
5y5(6 + -8y + y2) = 0
(6 * 5y5 + -8y * 5y5 + y2 * 5y5) = 0
(30y5 + -40y6 + 5y7) = 0

Solving
30y5 + -40y6 + 5y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y5'.
5y5(6 + -8y + y2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve:

Simplifying
y5 = 0

Solving
y5 = 0

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

Simplifying
y5 = 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 '(6 + -8y + y2)' equal to zero and attempt to solve:

Simplifying
6 + -8y + y2 = 0

Solving
6 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + -8y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8y + y2 = 0 + -6
-8y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8y + y2 = -6

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 = -6 + 16

Reorder the terms:
16 + -8y + y2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8y + y2 = 10

Factor a perfect square on the left side:
(y + -4)(y + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(y + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
y + -4 = 3.16227766

Simplifying
y + -4 = 3.16227766

Reorder the terms:
-4 + y = 3.16227766

Solving
-4 + y = 3.16227766

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 = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + y = 3.16227766 + 4
y = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
y = 7.16227766

Simplifying
y = 7.16227766

Subproblem 2
y + -4 = -3.16227766

Simplifying
y + -4 = -3.16227766

Reorder the terms:
-4 + y = -3.16227766

Solving
-4 + y = -3.16227766

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 = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + y = -3.16227766 + 4
y = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
y = 0.83772234

Simplifying
y = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.16227766, 0.83772234}
Solution
y = {7.16227766, 0.83772234}