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

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


Simplifying
An = n(n + -1)(n + -2) + 2n

Reorder the terms:
nA = n(-1 + n)(n + -2) + 2n

Reorder the terms:
nA = n(-1 + n)(-2 + n) + 2n

Multiply (-1 + n) * (-2 + n)
nA = n(-1(-2 + n) + n(-2 + n)) + 2n
nA = n((-2 * -1 + n * -1) + n(-2 + n)) + 2n
nA = n((2 + -1n) + n(-2 + n)) + 2n
nA = n(2 + -1n + (-2 * n + n * n)) + 2n
nA = n(2 + -1n + (-2n + n2)) + 2n

Combine like terms: -1n + -2n = -3n
nA = n(2 + -3n + n2) + 2n
nA = (2 * n + -3n * n + n2 * n) + 2n
nA = (2n + -3n2 + n3) + 2n

Reorder the terms:
nA = 2n + 2n + -3n2 + n3

Combine like terms: 2n + 2n = 4n
nA = 4n + -3n2 + n3

Solving
nA = 4n + -3n2 + n3

Solving for variable 'n'.

Reorder the terms:
-4n + nA + 3n2 + -1n3 = 4n + -3n2 + n3 + -4n + 3n2 + -1n3

Reorder the terms:
-4n + nA + 3n2 + -1n3 = 4n + -4n + -3n2 + 3n2 + n3 + -1n3

Combine like terms: 4n + -4n = 0
-4n + nA + 3n2 + -1n3 = 0 + -3n2 + 3n2 + n3 + -1n3
-4n + nA + 3n2 + -1n3 = -3n2 + 3n2 + n3 + -1n3

Combine like terms: -3n2 + 3n2 = 0
-4n + nA + 3n2 + -1n3 = 0 + n3 + -1n3
-4n + nA + 3n2 + -1n3 = n3 + -1n3

Combine like terms: n3 + -1n3 = 0
-4n + nA + 3n2 + -1n3 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4 + A + 3n + -1n2) = 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 '(-4 + A + 3n + -1n2)' equal to zero and attempt to solve:

Simplifying
-4 + A + 3n + -1n2 = 0

Solving
-4 + A + 3n + -1n2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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