(k-5)(k-2)=0

Solution for (k-5)(k-2)=0 equation:

Simplifying
(k + -5)(k + -2) = 0

Reorder the terms:
(-5 + k)(k + -2) = 0

Reorder the terms:
(-5 + k)(-2 + k) = 0

Multiply (-5 + k) * (-2 + k)
(-5(-2 + k) + k(-2 + k)) = 0
((-2 * -5 + k * -5) + k(-2 + k)) = 0
((10 + -5k) + k(-2 + k)) = 0
(10 + -5k + (-2 * k + k * k)) = 0
(10 + -5k + (-2k + k2)) = 0

Combine like terms: -5k + -2k = -7k
(10 + -7k + k2) = 0

Solving
10 + -7k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -1k)(5 + -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 '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {2, 5}