8k^2+13k-6=0

Solution for 8k^2+13k-6=0 equation:

Simplifying
8k2 + 13k + -6 = 0

Reorder the terms:
-6 + 13k + 8k2 = 0

Solving
-6 + 13k + 8k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-2 + -1k)(3 + -8k) = 0

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 '(3 + -8k)' equal to zero and attempt to solve:

Simplifying
3 + -8k = 0

Solving
3 + -8k = 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 + -8k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8k = 0 + -3
-8k = 0 + -3

Combine like terms: 0 + -3 = -3
-8k = -3

Divide each side by '-8'.
k = 0.375

Simplifying
k = 0.375
Solution
k = {-2, 0.375}