(4k+8)(2k-6)=0

Solution for (4k+8)(2k-6)=0 equation:

Simplifying
(4k + 8)(2k + -6) = 0

Reorder the terms:
(8 + 4k)(2k + -6) = 0

Reorder the terms:
(8 + 4k)(-6 + 2k) = 0

Multiply (8 + 4k) * (-6 + 2k)
(8(-6 + 2k) + 4k * (-6 + 2k)) = 0
((-6 * 8 + 2k * 8) + 4k * (-6 + 2k)) = 0
((-48 + 16k) + 4k * (-6 + 2k)) = 0
(-48 + 16k + (-6 * 4k + 2k * 4k)) = 0
(-48 + 16k + (-24k + 8k2)) = 0

Combine like terms: 16k + -24k = -8k
(-48 + -8k + 8k2) = 0

Solving
-48 + -8k + 8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + -1k + k2) = 0

Factor a trinomial.
8((-2 + -1k)(3 + -1k)) = 0

Ignore the factor 8.
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}