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Simplifying 0 = 3k2 + 12k + 9 Reorder the terms: 0 = 9 + 12k + 3k2 Solving 0 = 9 + 12k + 3k2 Solving for variable 'k'. Combine like terms: 0 + -9 = -9 -9 + -12k + -3k2 = 9 + 12k + 3k2 + -9 + -12k + -3k2 Reorder the terms: -9 + -12k + -3k2 = 9 + -9 + 12k + -12k + 3k2 + -3k2 Combine like terms: 9 + -9 = 0 -9 + -12k + -3k2 = 0 + 12k + -12k + 3k2 + -3k2 -9 + -12k + -3k2 = 12k + -12k + 3k2 + -3k2 Combine like terms: 12k + -12k = 0 -9 + -12k + -3k2 = 0 + 3k2 + -3k2 -9 + -12k + -3k2 = 3k2 + -3k2 Combine like terms: 3k2 + -3k2 = 0 -9 + -12k + -3k2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(3 + 4k + k2) = 0 Factor a trinomial. -3((3 + k)(1 + k)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(3 + k)' equal to zero and attempt to solve: Simplifying 3 + k = 0 Solving 3 + k = 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 + k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + k = 0 + -3 k = 0 + -3 Combine like terms: 0 + -3 = -3 k = -3 Simplifying k = -3Subproblem 2
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 = -1Solution
k = {-3, -1}
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