-2y^3(2y^2+5y-6)=

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

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

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

Solving
12y3 + -10y4 + -4y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y3'.
2y3(6 + -5y + -2y2) = 0

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

Simplifying
6 + -5y + -2y2 = 0

Solving
6 + -5y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + 2.5y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 2.5y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 2.5y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2.5y + y2 = 0 + 3
2.5y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
2.5y + y2 = 3

The y term is 2.5y.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5y + 1.5625 + y2 = 3 + 1.5625

Reorder the terms:
1.5625 + 2.5y + y2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + 2.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + 1.25)(y + 1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + 1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
y + 1.25 = 2.136000936

Simplifying
y + 1.25 = 2.136000936

Reorder the terms:
1.25 + y = 2.136000936

Solving
1.25 + y = 2.136000936

Solving for variable 'y'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + y = 2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + y = 2.136000936 + -1.25
y = 2.136000936 + -1.25

Combine like terms: 2.136000936 + -1.25 = 0.886000936
y = 0.886000936

Simplifying
y = 0.886000936

Subproblem 2
y + 1.25 = -2.136000936

Simplifying
y + 1.25 = -2.136000936

Reorder the terms:
1.25 + y = -2.136000936

Solving
1.25 + y = -2.136000936

Solving for variable 'y'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + y = -2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + y = -2.136000936 + -1.25
y = -2.136000936 + -1.25

Combine like terms: -2.136000936 + -1.25 = -3.386000936
y = -3.386000936

Simplifying
y = -3.386000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.886000936, -3.386000936}
Solution
y = {0.886000936, -3.386000936}