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Simplifying (3k + -9)(5k + 8) = 0 Reorder the terms: (-9 + 3k)(5k + 8) = 0 Reorder the terms: (-9 + 3k)(8 + 5k) = 0 Multiply (-9 + 3k) * (8 + 5k) (-9(8 + 5k) + 3k * (8 + 5k)) = 0 ((8 * -9 + 5k * -9) + 3k * (8 + 5k)) = 0 ((-72 + -45k) + 3k * (8 + 5k)) = 0 (-72 + -45k + (8 * 3k + 5k * 3k)) = 0 (-72 + -45k + (24k + 15k2)) = 0 Combine like terms: -45k + 24k = -21k (-72 + -21k + 15k2) = 0 Solving -72 + -21k + 15k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + -7k + 5k2) = 0 Factor a trinomial. 3((-8 + -5k)(3 + -1k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -5k)' equal to zero and attempt to solve: Simplifying -8 + -5k = 0 Solving -8 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5k = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5k = 0 + 8 -5k = 0 + 8 Combine like terms: 0 + 8 = 8 -5k = 8 Divide each side by '-5'. k = -1.6 Simplifying k = -1.6Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 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 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {-1.6, 3}
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