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Simplifying (3k + 8)(2k + 5) = 0 Reorder the terms: (8 + 3k)(2k + 5) = 0 Reorder the terms: (8 + 3k)(5 + 2k) = 0 Multiply (8 + 3k) * (5 + 2k) (8(5 + 2k) + 3k * (5 + 2k)) = 0 ((5 * 8 + 2k * 8) + 3k * (5 + 2k)) = 0 ((40 + 16k) + 3k * (5 + 2k)) = 0 (40 + 16k + (5 * 3k + 2k * 3k)) = 0 (40 + 16k + (15k + 6k2)) = 0 Combine like terms: 16k + 15k = 31k (40 + 31k + 6k2) = 0 Solving 40 + 31k + 6k2 = 0 Solving for variable 'k'. Factor a trinomial. (8 + 3k)(5 + 2k) = 0Subproblem 1
Set the factor '(8 + 3k)' equal to zero and attempt to solve: Simplifying 8 + 3k = 0 Solving 8 + 3k = 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 + 3k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3k = 0 + -8 3k = 0 + -8 Combine like terms: 0 + -8 = -8 3k = -8 Divide each side by '3'. k = -2.666666667 Simplifying k = -2.666666667Subproblem 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 = {-2.666666667, -2.5}
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