6k^2-53k-9=0

Solution for 6k^2-53k-9=0 equation:

Simplifying
6k2 + -53k + -9 = 0

Reorder the terms:
-9 + -53k + 6k2 = 0

Solving
-9 + -53k + 6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -6k)(9 + -1k) = 0

Subproblem 1
Set the factor '(-1 + -6k)' equal to zero and attempt to solve:

Simplifying
-1 + -6k = 0

Solving
-1 + -6k = 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 + -6k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6k = 0 + 1
-6k = 0 + 1

Combine like terms: 0 + 1 = 1
-6k = 1

Divide each side by '-6'.
k = -0.1666666667

Simplifying
k = -0.1666666667
Subproblem 2
Set the factor '(9 + -1k)' equal to zero and attempt to solve:

Simplifying
9 + -1k = 0

Solving
9 + -1k = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1k = 0 + -9
-1k = 0 + -9

Combine like terms: 0 + -9 = -9
-1k = -9

Divide each side by '-1'.
k = 9

Simplifying
k = 9
Solution
k = {-0.1666666667, 9}