n(n+1)(n-6)=0

Solution for n(n+1)(n-6)=0 equation:

Simplifying
n(n + 1)(n + -6) = 0

Reorder the terms:
n(1 + n)(n + -6) = 0

Reorder the terms:
n(1 + n)(-6 + n) = 0

Multiply (1 + n) * (-6 + n)
n(1(-6 + n) + n(-6 + n)) = 0
n((-6 * 1 + n * 1) + n(-6 + n)) = 0
n((-6 + 1n) + n(-6 + n)) = 0
n(-6 + 1n + (-6 * n + n * n)) = 0
n(-6 + 1n + (-6n + n2)) = 0

Combine like terms: 1n + -6n = -5n
n(-6 + -5n + n2) = 0
(-6 * n + -5n * n + n2 * n) = 0
(-6n + -5n2 + n3) = 0

Solving
-6n + -5n2 + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6 + -5n + n2) = 0

Factor a trinomial.
n((-1 + -1n)(6 + -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 '(-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
Subproblem 3
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {0, -1, 6}