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Simplifying (4k + -5)(2k + 6) = 0 Reorder the terms: (-5 + 4k)(2k + 6) = 0 Reorder the terms: (-5 + 4k)(6 + 2k) = 0 Multiply (-5 + 4k) * (6 + 2k) (-5(6 + 2k) + 4k * (6 + 2k)) = 0 ((6 * -5 + 2k * -5) + 4k * (6 + 2k)) = 0 ((-30 + -10k) + 4k * (6 + 2k)) = 0 (-30 + -10k + (6 * 4k + 2k * 4k)) = 0 (-30 + -10k + (24k + 8k2)) = 0 Combine like terms: -10k + 24k = 14k (-30 + 14k + 8k2) = 0 Solving -30 + 14k + 8k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 7k + 4k2) = 0 Factor a trinomial. 2((-3 + -1k)(5 + -4k)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(5 + -4k)' equal to zero and attempt to solve: Simplifying 5 + -4k = 0 Solving 5 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4k = 0 + -5 -4k = 0 + -5 Combine like terms: 0 + -5 = -5 -4k = -5 Divide each side by '-4'. k = 1.25 Simplifying k = 1.25Solution
k = {-3, 1.25}
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