n^3+n^2+n=0

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

Simplifying
n3 + n2 + n = 0

Reorder the terms:
n + n2 + n3 = 0

Solving
n + n2 + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + n + n2) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(1 + n + n2)' equal to zero and attempt to solve:

Simplifying
1 + n + n2 = 0

Solving
1 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n + n2 = 0 + -1
n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
n + n2 = -1

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = -1 + 0.25

Reorder the terms:
0.25 + n + n2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + n + n2 = -0.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -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
n = {0}