15y^3+12y^2+6y=

Solution for 15y^3+12y^2+6y= equation:

Simplifying
15y3 + 12y2 + 6y = 0

Reorder the terms:
6y + 12y2 + 15y3 = 0

Solving
6y + 12y2 + 15y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(2 + 4y + 5y2) = 0

Ignore the factor 3.
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 + 4y + 5y2)' equal to zero and attempt to solve:

Simplifying
2 + 4y + 5y2 = 0

Solving
2 + 4y + 5y2 = 0

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

Divide each side by '5'.
0.4 + 0.8y + y2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 0.8y + -0.4 + y2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 0.8y + y2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 0.8y + y2 = 0 + -0.4
0.8y + y2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
0.8y + y2 = -0.4

The y term is 0.8y.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8y + 0.16 + y2 = -0.4 + 0.16

Reorder the terms:
0.16 + 0.8y + y2 = -0.4 + 0.16

Combine like terms: -0.4 + 0.16 = -0.24
0.16 + 0.8y + y2 = -0.24

Factor a perfect square on the left side:
(y + 0.4)(y + 0.4) = -0.24

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}