(k-2)(k-3)=

Solution for (k-2)(k-3)= equation:

Simplifying
(k + -2)(k + -3) = 0

Reorder the terms:
(-2 + k)(k + -3) = 0

Reorder the terms:
(-2 + k)(-3 + k) = 0

Multiply (-2 + k) * (-3 + k)
(-2(-3 + k) + k(-3 + k)) = 0
((-3 * -2 + k * -2) + k(-3 + k)) = 0
((6 + -2k) + k(-3 + k)) = 0
(6 + -2k + (-3 * k + k * k)) = 0
(6 + -2k + (-3k + k2)) = 0

Combine like terms: -2k + -3k = -5k
(6 + -5k + k2) = 0

Solving
6 + -5k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -1k)(3 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {2, 3}