2k^2-3k-65=0

Solution for 2k^2-3k-65=0 equation:

Simplifying
2k2 + -3k + -65 = 0

Reorder the terms:
-65 + -3k + 2k2 = 0

Solving
-65 + -3k + 2k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -1k)(13 + -2k) = 0

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

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 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 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(13 + -2k)' equal to zero and attempt to solve:

Simplifying
13 + -2k = 0

Solving
13 + -2k = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2k = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2k = 0 + -13
-2k = 0 + -13

Combine like terms: 0 + -13 = -13
-2k = -13

Divide each side by '-2'.
k = 6.5

Simplifying
k = 6.5
Solution
k = {-5, 6.5}