12y^3-2y^2+15y=0

Solution for 12y^3-2y^2+15y=0 equation:

Simplifying
12y3 + -2y2 + 15y = 0

Reorder the terms:
15y + -2y2 + 12y3 = 0

Solving
15y + -2y2 + 12y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(15 + -2y + 12y2) = 0

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 '(15 + -2y + 12y2)' equal to zero and attempt to solve:

Simplifying
15 + -2y + 12y2 = 0

Solving
15 + -2y + 12y2 = 0

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

Divide each side by '12'.
1.25 + -0.1666666667y + y2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -0.1666666667y + -1.25 + y2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -0.1666666667y + y2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.1666666667y + y2 = 0 + -1.25
-0.1666666667y + y2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-0.1666666667y + y2 = -1.25

The y term is -0.1666666667y.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667y + 0.006944444447 + y2 = -1.25 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667y + y2 = -1.25 + 0.006944444447

Combine like terms: -1.25 + 0.006944444447 = -1.243055555553
0.006944444447 + -0.1666666667y + y2 = -1.243055555553

Factor a perfect square on the left side:
(y + -0.08333333335)(y + -0.08333333335) = -1.243055555553

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}