25k^2-20k-60=0

Solution for 25k^2-20k-60=0 equation:

Simplifying
25k2 + -20k + -60 = 0

Reorder the terms:
-60 + -20k + 25k2 = 0

Solving
-60 + -20k + 25k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + -4k + 5k2) = 0

Factor a trinomial.
5((-6 + -5k)(2 + -1k)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -5k)' equal to zero and attempt to solve:

Simplifying
-6 + -5k = 0

Solving
-6 + -5k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5k = 0 + 6
-5k = 0 + 6

Combine like terms: 0 + 6 = 6
-5k = 6

Divide each side by '-5'.
k = -1.2

Simplifying
k = -1.2
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-1.2, 2}