0=n(n+1)(n+2)(n+3)

Solution for 0=n(n+1)(n+2)(n+3) equation:

Simplifying
0 = n(n + 1)(n + 2)(n + 3)

Reorder the terms:
0 = n(1 + n)(n + 2)(n + 3)

Reorder the terms:
0 = n(1 + n)(2 + n)(n + 3)

Reorder the terms:
0 = n(1 + n)(2 + n)(3 + n)

Multiply (1 + n) * (2 + n)
0 = n(1(2 + n) + n(2 + n))(3 + n)
0 = n((2 * 1 + n * 1) + n(2 + n))(3 + n)
0 = n((2 + 1n) + n(2 + n))(3 + n)
0 = n(2 + 1n + (2 * n + n * n))(3 + n)
0 = n(2 + 1n + (2n + n2))(3 + n)

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

Multiply (2 + 3n + n2) * (3 + n)
0 = n(2(3 + n) + 3n * (3 + n) + n2(3 + n))
0 = n((3 * 2 + n * 2) + 3n * (3 + n) + n2(3 + n))
0 = n((6 + 2n) + 3n * (3 + n) + n2(3 + n))
0 = n(6 + 2n + (3 * 3n + n * 3n) + n2(3 + n))
0 = n(6 + 2n + (9n + 3n2) + n2(3 + n))
0 = n(6 + 2n + 9n + 3n2 + (3 * n2 + n * n2))
0 = n(6 + 2n + 9n + 3n2 + (3n2 + n3))

Combine like terms: 2n + 9n = 11n
0 = n(6 + 11n + 3n2 + 3n2 + n3)

Combine like terms: 3n2 + 3n2 = 6n2
0 = n(6 + 11n + 6n2 + n3)
0 = (6 * n + 11n * n + 6n2 * n + n3 * n)
0 = (6n + 11n2 + 6n3 + n4)

Solving
0 = 6n + 11n2 + 6n3 + n4

Solving for variable 'n'.
Remove the zero:
-6n + -11n2 + -6n3 + -1n4 = 6n + 11n2 + 6n3 + n4 + -6n + -11n2 + -6n3 + -1n4

Reorder the terms:
-6n + -11n2 + -6n3 + -1n4 = 6n + -6n + 11n2 + -11n2 + 6n3 + -6n3 + n4 + -1n4

Combine like terms: 6n + -6n = 0
-6n + -11n2 + -6n3 + -1n4 = 0 + 11n2 + -11n2 + 6n3 + -6n3 + n4 + -1n4
-6n + -11n2 + -6n3 + -1n4 = 11n2 + -11n2 + 6n3 + -6n3 + n4 + -1n4

Combine like terms: 11n2 + -11n2 = 0
-6n + -11n2 + -6n3 + -1n4 = 0 + 6n3 + -6n3 + n4 + -1n4
-6n + -11n2 + -6n3 + -1n4 = 6n3 + -6n3 + n4 + -1n4

Combine like terms: 6n3 + -6n3 = 0
-6n + -11n2 + -6n3 + -1n4 = 0 + n4 + -1n4
-6n + -11n2 + -6n3 + -1n4 = n4 + -1n4

Combine like terms: n4 + -1n4 = 0
-6n + -11n2 + -6n3 + -1n4 = 0

Factor out the Greatest Common Factor (GCF), '-1n'.
-1n(6 + 11n + 6n2 + n3) = 0

Ignore the factor -1.
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 '(6 + 11n + 6n2 + n3)' equal to zero and attempt to solve:

Simplifying
6 + 11n + 6n2 + n3 = 0

Solving
6 + 11n + 6n2 + n3 = 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}