(k-8)(2k-12)=0

Solution for (k-8)(2k-12)=0 equation:

Simplifying
(k + -8)(2k + -12) = 0

Reorder the terms:
(-8 + k)(2k + -12) = 0

Reorder the terms:
(-8 + k)(-12 + 2k) = 0

Multiply (-8 + k) * (-12 + 2k)
(-8(-12 + 2k) + k(-12 + 2k)) = 0
((-12 * -8 + 2k * -8) + k(-12 + 2k)) = 0
((96 + -16k) + k(-12 + 2k)) = 0
(96 + -16k + (-12 * k + 2k * k)) = 0
(96 + -16k + (-12k + 2k2)) = 0

Combine like terms: -16k + -12k = -28k
(96 + -28k + 2k2) = 0

Solving
96 + -28k + 2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + -14k + k2) = 0

Factor a trinomial.
2((6 + -1k)(8 + -1k)) = 0

Ignore the factor 2.
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 '(8 + -1k)' equal to zero and attempt to solve:

Simplifying
8 + -1k = 0

Solving
8 + -1k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1k = 0 + -8
-1k = 0 + -8

Combine like terms: 0 + -8 = -8
-1k = -8

Divide each side by '-1'.
k = 8

Simplifying
k = 8
Solution
k = {6, 8}