6k^2+19k+15=0

Solution for 6k^2+19k+15=0 equation:

Simplifying
6k2 + 19k + 15 = 0

Reorder the terms:
15 + 19k + 6k2 = 0

Solving
15 + 19k + 6k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(5 + 3k)' equal to zero and attempt to solve:

Simplifying
5 + 3k = 0

Solving
5 + 3k = 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 + 3k = 0 + -5

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

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

Divide each side by '3'.
k = -1.666666667

Simplifying
k = -1.666666667
Subproblem 2
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

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

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Solution
k = {-1.666666667, -1.5}