(k-2)(k+6)=0

Solution for (k-2)(k+6)=0 equation:

Simplifying
(k + -2)(k + 6) = 0

Reorder the terms:
(-2 + k)(k + 6) = 0

Reorder the terms:
(-2 + k)(6 + k) = 0

Multiply (-2 + k) * (6 + k)
(-2(6 + k) + k(6 + k)) = 0
((6 * -2 + k * -2) + k(6 + k)) = 0
((-12 + -2k) + k(6 + k)) = 0
(-12 + -2k + (6 * k + k * k)) = 0
(-12 + -2k + (6k + k2)) = 0

Combine like terms: -2k + 6k = 4k
(-12 + 4k + k2) = 0

Solving
-12 + 4k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-6 + -1k)(2 + -1k) = 0

Subproblem 1
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
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 = {-6, 2}