40k^2+124k+60=0

Solution for 40k^2+124k+60=0 equation:

Simplifying
40k2 + 124k + 60 = 0

Reorder the terms:
60 + 124k + 40k2 = 0

Solving
60 + 124k + 40k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 31k + 10k2) = 0

Factor a trinomial.
4((5 + 2k)(3 + 5k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + 2k)' equal to zero and attempt to solve:

Simplifying
5 + 2k = 0

Solving
5 + 2k = 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 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
Subproblem 2
Set the factor '(3 + 5k)' equal to zero and attempt to solve:

Simplifying
3 + 5k = 0

Solving
3 + 5k = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5k = 0 + -3
5k = 0 + -3

Combine like terms: 0 + -3 = -3
5k = -3

Divide each side by '5'.
k = -0.6

Simplifying
k = -0.6
Solution
k = {-2.5, -0.6}