x(n-1)(n-2)=0

Solution for x(n-1)(n-2)=0 equation:

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

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

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

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

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

Reorder the terms:
(-3nx + n2x + 2x) = 0
(-3nx + n2x + 2x) = 0

Solving
-3nx + n2x + 2x = 0

Solving for variable 'n'.

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

Factor a trinomial.
x((n + -2)(n + -1)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(n + -2)' equal to zero and attempt to solve:

Simplifying
n + -2 = 0

Reorder the terms:
-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 '(n + -1)' equal to zero and attempt to solve:

Simplifying
n + -1 = 0

Reorder the terms:
-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 = {2, 1}