9k^2+15k+6=0

Solution for 9k^2+15k+6=0 equation:

Simplifying
9k2 + 15k + 6 = 0

Reorder the terms:
6 + 15k + 9k2 = 0

Solving
6 + 15k + 9k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 5k + 3k2) = 0

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

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

Simplifying
1 + k = 0

Solving
1 + k = 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 + k = 0 + -1

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

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

Simplifying
k = -1
Subproblem 2
Set the factor '(2 + 3k)' equal to zero and attempt to solve:

Simplifying
2 + 3k = 0

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

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

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

Divide each side by '3'.
k = -0.6666666667

Simplifying
k = -0.6666666667
Solution
k = {-1, -0.6666666667}