n(n+1)(n+2)=0

Solution for n(n+1)(n+2)=0 equation:

Simplifying
n(n + 1)(n + 2) = 0

Reorder the terms:
n(1 + n)(n + 2) = 0

Reorder the terms:
n(1 + n)(2 + n) = 0

Multiply (1 + n) * (2 + n)
n(1(2 + n) + n(2 + n)) = 0
n((2 * 1 + n * 1) + n(2 + n)) = 0
n((2 + 1n) + n(2 + n)) = 0
n(2 + 1n + (2 * n + n * n)) = 0
n(2 + 1n + (2n + n2)) = 0

Combine like terms: 1n + 2n = 3n
n(2 + 3n + n2) = 0
(2 * n + 3n * n + n2 * n) = 0
(2n + 3n2 + n3) = 0

Solving
2n + 3n2 + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(2 + 3n + n2) = 0

Factor a trinomial.
n((2 + n)(1 + n)) = 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 + 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
Subproblem 3
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

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