z^3+3z^2+3z=0

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

Simplifying
z3 + 3z2 + 3z = 0

Reorder the terms:
3z + 3z2 + z3 = 0

Solving
3z + 3z2 + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(3 + 3z + z2) = 0

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(3 + 3z + z2)' equal to zero and attempt to solve:

Simplifying
3 + 3z + z2 = 0

Solving
3 + 3z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 3z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + 3z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3z + z2 = 0 + -3
3z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
3z + z2 = -3

The z term is 3z.  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.
3z + 2.25 + z2 = -3 + 2.25

Reorder the terms:
2.25 + 3z + z2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + 3z + z2 = -0.75

Factor a perfect square on the left side:
(z + 1.5)(z + 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
z = {0}