3k^2-8k-115=0

Solution for 3k^2-8k-115=0 equation:

Simplifying
3k2 + -8k + -115 = 0

Reorder the terms:
-115 + -8k + 3k2 = 0

Solving
-115 + -8k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -1k)(23 + -3k) = 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 '(23 + -3k)' equal to zero and attempt to solve:

Simplifying
23 + -3k = 0

Solving
23 + -3k = 0

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

Add '-23' to each side of the equation.
23 + -23 + -3k = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -3k = 0 + -23
-3k = 0 + -23

Combine like terms: 0 + -23 = -23
-3k = -23

Divide each side by '-3'.
k = 7.666666667

Simplifying
k = 7.666666667
Solution
k = {-5, 7.666666667}