30y^3-6y^2+12y=0

Solution for 30y^3-6y^2+12y=0 equation:

Simplifying
30y3 + -6y2 + 12y = 0

Reorder the terms:
12y + -6y2 + 30y3 = 0

Solving
12y + -6y2 + 30y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6y'.
6y(2 + -1y + 5y2) = 0

Ignore the factor 6.
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 '(2 + -1y + 5y2)' equal to zero and attempt to solve:

Simplifying
2 + -1y + 5y2 = 0

Solving
2 + -1y + 5y2 = 0

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

Divide each side by '5'.
0.4 + -0.2y + y2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -0.2y + -0.4 + y2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -0.2y + y2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -0.2y + y2 = 0 + -0.4
-0.2y + y2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-0.2y + y2 = -0.4

The y term is -0.2y.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2y + 0.01 + y2 = -0.4 + 0.01

Reorder the terms:
0.01 + -0.2y + y2 = -0.4 + 0.01

Combine like terms: -0.4 + 0.01 = -0.39
0.01 + -0.2y + y2 = -0.39

Factor a perfect square on the left side:
(y + -0.1)(y + -0.1) = -0.39

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}