n^3-2n^2(n+1)=

Solution for n^3-2n^2(n+1)= equation:

Simplifying
n3 + -2n2(n + 1) = 0

Reorder the terms:
n3 + -2n2(1 + n) = 0
n3 + (1 * -2n2 + n * -2n2) = 0
n3 + (-2n2 + -2n3) = 0

Reorder the terms:
-2n2 + n3 + -2n3 = 0

Combine like terms: n3 + -2n3 = -1n3
-2n2 + -1n3 = 0

Solving
-2n2 + -1n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1n2'.
-1n2(2 + n) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {0, -2}