6k^2-7k-5=0

Solution for 6k^2-7k-5=0 equation:

Simplifying
6k2 + -7k + -5 = 0

Reorder the terms:
-5 + -7k + 6k2 = 0

Solving
-5 + -7k + 6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -2k)(5 + -3k) = 0

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

Simplifying
-1 + -2k = 0

Solving
-1 + -2k = 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 + -2k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2k = 0 + 1
-2k = 0 + 1

Combine like terms: 0 + 1 = 1
-2k = 1

Divide each side by '-2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve:

Simplifying
5 + -3k = 0

Solving
5 + -3k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3k = 0 + -5
-3k = 0 + -5

Combine like terms: 0 + -5 = -5
-3k = -5

Divide each side by '-3'.
k = 1.666666667

Simplifying
k = 1.666666667
Solution
k = {-0.5, 1.666666667}