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Simplifying (2k + -5)(3k + 6) = 0 Reorder the terms: (-5 + 2k)(3k + 6) = 0 Reorder the terms: (-5 + 2k)(6 + 3k) = 0 Multiply (-5 + 2k) * (6 + 3k) (-5(6 + 3k) + 2k * (6 + 3k)) = 0 ((6 * -5 + 3k * -5) + 2k * (6 + 3k)) = 0 ((-30 + -15k) + 2k * (6 + 3k)) = 0 (-30 + -15k + (6 * 2k + 3k * 2k)) = 0 (-30 + -15k + (12k + 6k2)) = 0 Combine like terms: -15k + 12k = -3k (-30 + -3k + 6k2) = 0 Solving -30 + -3k + 6k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -1k + 2k2) = 0 Factor a trinomial. 3((-2 + -1k)(5 + -2k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(5 + -2k)' equal to zero and attempt to solve: Simplifying 5 + -2k = 0 Solving 5 + -2k = 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 + -2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2k = 0 + -5 -2k = 0 + -5 Combine like terms: 0 + -5 = -5 -2k = -5 Divide each side by '-2'. k = 2.5 Simplifying k = 2.5Solution
k = {-2, 2.5}
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