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Simplifying (5k + 4)(6k + 9) = 0 Reorder the terms: (4 + 5k)(6k + 9) = 0 Reorder the terms: (4 + 5k)(9 + 6k) = 0 Multiply (4 + 5k) * (9 + 6k) (4(9 + 6k) + 5k * (9 + 6k)) = 0 ((9 * 4 + 6k * 4) + 5k * (9 + 6k)) = 0 ((36 + 24k) + 5k * (9 + 6k)) = 0 (36 + 24k + (9 * 5k + 6k * 5k)) = 0 (36 + 24k + (45k + 30k2)) = 0 Combine like terms: 24k + 45k = 69k (36 + 69k + 30k2) = 0 Solving 36 + 69k + 30k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 23k + 10k2) = 0 Factor a trinomial. 3((3 + 2k)(4 + 5k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 2k)' equal to zero and attempt to solve: Simplifying 3 + 2k = 0 Solving 3 + 2k = 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 + 2k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2k = 0 + -3 2k = 0 + -3 Combine like terms: 0 + -3 = -3 2k = -3 Divide each side by '2'. k = -1.5 Simplifying k = -1.5Subproblem 2
Set the factor '(4 + 5k)' equal to zero and attempt to solve: Simplifying 4 + 5k = 0 Solving 4 + 5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5k = 0 + -4 5k = 0 + -4 Combine like terms: 0 + -4 = -4 5k = -4 Divide each side by '5'. k = -0.8 Simplifying k = -0.8Solution
k = {-1.5, -0.8}
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