5k^2-6k-11=0

Solution for 5k^2-6k-11=0 equation:

Simplifying
5k2 + -6k + -11 = 0

Reorder the terms:
-11 + -6k + 5k2 = 0

Solving
-11 + -6k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -1k)(11 + -5k) = 0

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

Simplifying
-1 + -1k = 0

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

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

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

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

Simplifying
k = -1
Subproblem 2
Set the factor '(11 + -5k)' equal to zero and attempt to solve:

Simplifying
11 + -5k = 0

Solving
11 + -5k = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5k = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5k = 0 + -11
-5k = 0 + -11

Combine like terms: 0 + -11 = -11
-5k = -11

Divide each side by '-5'.
k = 2.2

Simplifying
k = 2.2
Solution
k = {-1, 2.2}