-2y^4(5y^3-6y^2-4y)=0

Solution for -2y^4(5y^3-6y^2-4y)=0 equation:

Simplifying
-2y4(5y3 + -6y2 + -4y) = 0

Reorder the terms:
-2y4(-4y + -6y2 + 5y3) = 0
(-4y * -2y4 + -6y2 * -2y4 + 5y3 * -2y4) = 0
(8y5 + 12y6 + -10y7) = 0

Solving
8y5 + 12y6 + -10y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y5'.
2y5(4 + 6y + -5y2) = 0

Ignore the factor 2.
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 '(4 + 6y + -5y2)' equal to zero and attempt to solve:

Simplifying
4 + 6y + -5y2 = 0

Solving
4 + 6y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.8 + -1.2y + y2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.2y + 0.8 + y2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.2y + y2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.2y + y2 = 0 + 0.8
-1.2y + y2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.2y + y2 = 0.8

The y term is -1.2y.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2y + 0.36 + y2 = 0.8 + 0.36

Reorder the terms:
0.36 + -1.2y + y2 = 0.8 + 0.36

Combine like terms: 0.8 + 0.36 = 1.16
0.36 + -1.2y + y2 = 1.16

Factor a perfect square on the left side:
(y + -0.6)(y + -0.6) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(y + -0.6) equal to 1.077032961 and -1.077032961.

Subproblem 1
y + -0.6 = 1.077032961

Simplifying
y + -0.6 = 1.077032961

Reorder the terms:
-0.6 + y = 1.077032961

Solving
-0.6 + y = 1.077032961

Solving for variable 'y'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + y = 1.077032961 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + y = 1.077032961 + 0.6
y = 1.077032961 + 0.6

Combine like terms: 1.077032961 + 0.6 = 1.677032961
y = 1.677032961

Simplifying
y = 1.677032961

Subproblem 2
y + -0.6 = -1.077032961

Simplifying
y + -0.6 = -1.077032961

Reorder the terms:
-0.6 + y = -1.077032961

Solving
-0.6 + y = -1.077032961

Solving for variable 'y'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + y = -1.077032961 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + y = -1.077032961 + 0.6
y = -1.077032961 + 0.6

Combine like terms: -1.077032961 + 0.6 = -0.477032961
y = -0.477032961

Simplifying
y = -0.477032961

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.677032961, -0.477032961}
Solution
y = {1.677032961, -0.477032961}