4k^2-24k=64

Solution for 4k^2-24k=64 equation:

Simplifying
4k2 + -24k = 64

Reorder the terms:
-24k + 4k2 = 64

Solving
-24k + 4k2 = 64

Solving for variable 'k'.

Reorder the terms:
-64 + -24k + 4k2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + -24k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -6k + k2) = 0

Factor a trinomial.
4((-2 + -1k)(8 + -1k)) = 0

Ignore the factor 4.
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 '(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 = {-2, 8}