Simplifying
3k2 + 18k + 15 = 0

Reorder the terms:
15 + 18k + 3k2 = 0

Solving
15 + 18k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 6k + k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 6k + k2)' equal to zero and attempt to solve:

Simplifying
5 + 6k + k2 = 0

Solving
5 + 6k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 6k + -5 + k2 = 0 + -5

Reorder the terms:
5 + -5 + 6k + k2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6k + k2 = 0 + -5
6k + k2 = 0 + -5

Combine like terms: 0 + -5 = -5
6k + k2 = -5

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = -5 + 9

Reorder the terms:
9 + 6k + k2 = -5 + 9

Combine like terms: -5 + 9 = 4
9 + 6k + k2 = 4

Factor a perfect square on the left side:
(k + 3)(k + 3) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(k + 3) equal to 2 and -2.

Subproblem 1
k + 3 = 2

Simplifying
k + 3 = 2

Reorder the terms:
3 + k = 2

Solving
3 + k = 2

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = 2 + -3

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

Combine like terms: 2 + -3 = -1
k = -1

Simplifying
k = -1

Subproblem 2
k + 3 = -2

Simplifying
k + 3 = -2

Reorder the terms:
3 + k = -2

Solving
3 + k = -2

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = -2 + -3

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

Combine like terms: -2 + -3 = -5
k = -5

Simplifying
k = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-1, -5}
Solution
k = {-1, -5}