Simplifying
3k^{2} + 18k + 15 = 0
Reorder the terms:
15 + 18k + 3k^{2} = 0
Solving
15 + 18k + 3k^{2} = 0
Solving for variable 'k'.
Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 6k + k^{2}) = 0
Ignore the factor 3.
#### Subproblem 1

Set the factor '(5 + 6k + k^{2})' equal to zero and attempt to solve:
Simplifying
5 + 6k + k^{2} = 0
Solving
5 + 6k + k^{2} = 0
Begin completing the square.
Move the constant term to the right:
Add '-5' to each side of the equation.
5 + 6k + -5 + k^{2} = 0 + -5
Reorder the terms:
5 + -5 + 6k + k^{2} = 0 + -5
Combine like terms: 5 + -5 = 0
0 + 6k + k^{2} = 0 + -5
6k + k^{2} = 0 + -5
Combine like terms: 0 + -5 = -5
6k + k^{2} = -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 + k^{2} = -5 + 9
Reorder the terms:
9 + 6k + k^{2} = -5 + 9
Combine like terms: -5 + 9 = 4
9 + 6k + k^{2} = 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}