8k^2+22k-6=0

Solution for 8k^2+22k-6=0 equation:

Simplifying
8k2 + 22k + -6 = 0

Reorder the terms:
-6 + 22k + 8k2 = 0

Solving
-6 + 22k + 8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 11k + 4k2) = 0

Factor a trinomial.
2((-3 + -1k)(1 + -4k)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
k = {-3, 0.25}