8k^2-16k-64=0

Solution for 8k^2-16k-64=0 equation:

Simplifying
8k2 + -16k + -64 = 0

Reorder the terms:
-64 + -16k + 8k2 = 0

Solving
-64 + -16k + 8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-8 + -2k + k2) = 0

Factor a trinomial.
8((-2 + -1k)(4 + -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 '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-2, 4}