(k-2)(k-1)=

Solution for (k-2)(k-1)= equation:

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

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

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

Multiply (-2 + k) * (-1 + k)
(-2(-1 + k) + k(-1 + k)) = 0
((-1 * -2 + k * -2) + k(-1 + k)) = 0
((2 + -2k) + k(-1 + k)) = 0
(2 + -2k + (-1 * k + k * k)) = 0
(2 + -2k + (-1k + k2)) = 0

Combine like terms: -2k + -1k = -3k
(2 + -3k + k2) = 0

Solving
2 + -3k + k2 = 0

Solving for variable 'k'.

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

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

Divide each side by '-1'.
k = 1

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

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

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

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

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

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