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Simplifying (4k + -3)(3k + -9) = 0 Reorder the terms: (-3 + 4k)(3k + -9) = 0 Reorder the terms: (-3 + 4k)(-9 + 3k) = 0 Multiply (-3 + 4k) * (-9 + 3k) (-3(-9 + 3k) + 4k * (-9 + 3k)) = 0 ((-9 * -3 + 3k * -3) + 4k * (-9 + 3k)) = 0 ((27 + -9k) + 4k * (-9 + 3k)) = 0 (27 + -9k + (-9 * 4k + 3k * 4k)) = 0 (27 + -9k + (-36k + 12k2)) = 0 Combine like terms: -9k + -36k = -45k (27 + -45k + 12k2) = 0 Solving 27 + -45k + 12k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -15k + 4k2) = 0 Factor a trinomial. 3((3 + -4k)(3 + -1k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -4k)' equal to zero and attempt to solve: Simplifying 3 + -4k = 0 Solving 3 + -4k = 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 + -4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4k = 0 + -3 -4k = 0 + -3 Combine like terms: 0 + -3 = -3 -4k = -3 Divide each side by '-4'. k = 0.75 Simplifying k = 0.75Subproblem 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 = {0.75, 3}
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