(k-6)(k+5)=0

Solution for (k-6)(k+5)=0 equation:

Simplifying
(k + -6)(k + 5) = 0

Reorder the terms:
(-6 + k)(k + 5) = 0

Reorder the terms:
(-6 + k)(5 + k) = 0

Multiply (-6 + k) * (5 + k)
(-6(5 + k) + k(5 + k)) = 0
((5 * -6 + k * -6) + k(5 + k)) = 0
((-30 + -6k) + k(5 + k)) = 0
(-30 + -6k + (5 * k + k * k)) = 0
(-30 + -6k + (5k + k2)) = 0

Combine like terms: -6k + 5k = -1k
(-30 + -1k + k2) = 0

Solving
-30 + -1k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -1k)(6 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-5, 6}