8K^2-30K-8=0

Solution for 8K^2-30K-8=0 equation:

Simplifying
8K2 + -30K + -8 = 0

Reorder the terms:
-8 + -30K + 8K2 = 0

Solving
-8 + -30K + 8K2 = 0

Solving for variable 'K'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -15K + 4K2) = 0

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

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

Simplifying
-1 + -4K = 0

Solving
-1 + -4K = 0

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

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

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

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

Divide each side by '-4'.
K = -0.25

Simplifying
K = -0.25
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 = {-0.25, 4}