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

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

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

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

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

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

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

Solving
2 + -3n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

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