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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}
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