y^3+3y^2+3y=0

Solution for y^3+3y^2+3y=0 equation:

Simplifying
y3 + 3y2 + 3y = 0

Reorder the terms:
3y + 3y2 + y3 = 0

Solving
3y + 3y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + 3y + y2) = 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 '(3 + 3y + y2)' equal to zero and attempt to solve:

Simplifying
3 + 3y + y2 = 0

Solving
3 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = -3 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + 3y + y2 = -0.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = -0.75

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}