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

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

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

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

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

Reorder the terms:
-1n + -1n + n2 + n3 = 0

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

Solving
-2n + n2 + n3 = 0

Solving for variable 'n'.

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

Factor a trinomial.
n((-2 + -1n)(1 + -1n)) = 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 '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 3
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {0, -2, 1}