20k^2+64k-64=0

Solution for 20k^2+64k-64=0 equation:

Simplifying
20k2 + 64k + -64 = 0

Reorder the terms:
-64 + 64k + 20k2 = 0

Solving
-64 + 64k + 20k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 16k + 5k2) = 0

Factor a trinomial.
4((-4 + -1k)(4 + -5k)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -5k)' equal to zero and attempt to solve:

Simplifying
4 + -5k = 0

Solving
4 + -5k = 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 + -5k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5k = 0 + -4
-5k = 0 + -4

Combine like terms: 0 + -4 = -4
-5k = -4

Divide each side by '-5'.
k = 0.8

Simplifying
k = 0.8
Solution
k = {-4, 0.8}