-2y^3+4y^2-6y=

Solution for -2y^3+4y^2-6y= equation:

Simplifying
-2y3 + 4y2 + -6y = 0

Reorder the terms:
-6y + 4y2 + -2y3 = 0

Solving
-6y + 4y2 + -2y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-3 + 2y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-3 + 2y + -1y2)' equal to zero and attempt to solve:

Simplifying
-3 + 2y + -1y2 = 0

Solving
-3 + 2y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -2y + y2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -2y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y + y2 = 0 + -3
-2y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2y + y2 = -3

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

Add '1' to each side of the equation.
-2y + 1 + y2 = -3 + 1

Reorder the terms:
1 + -2y + y2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + -2y + y2 = -2

Factor a perfect square on the left side:
(y + -1)(y + -1) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}