30k^2-65k-40=0

Solution for 30k^2-65k-40=0 equation:

Simplifying
30k2 + -65k + -40 = 0

Reorder the terms:
-40 + -65k + 30k2 = 0

Solving
-40 + -65k + 30k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -13k + 6k2) = 0

Factor a trinomial.
5((-1 + -2k)(8 + -3k)) = 0

Ignore the factor 5.
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 '(8 + -3k)' equal to zero and attempt to solve:

Simplifying
8 + -3k = 0

Solving
8 + -3k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3k = 0 + -8
-3k = 0 + -8

Combine like terms: 0 + -8 = -8
-3k = -8

Divide each side by '-3'.
k = 2.666666667

Simplifying
k = 2.666666667
Solution
k = {-0.5, 2.666666667}