Z^3+3Z^2+3Z+3=3

Solution for Z^3+3Z^2+3Z+3=3 equation:

Simplifying
Z3 + 3Z2 + 3Z + 3 = 3

Reorder the terms:
3 + 3Z + 3Z2 + Z3 = 3

Add '-3' to each side of the equation.
3 + 3Z + 3Z2 + -3 + Z3 = 3 + -3

Reorder the terms:
3 + -3 + 3Z + 3Z2 + Z3 = 3 + -3

Combine like terms: 3 + -3 = 0
0 + 3Z + 3Z2 + Z3 = 3 + -3
3Z + 3Z2 + Z3 = 3 + -3

Combine like terms: 3 + -3 = 0
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}