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Simplifying (k + -5)(3k + -8) = 0 Reorder the terms: (-5 + k)(3k + -8) = 0 Reorder the terms: (-5 + k)(-8 + 3k) = 0 Multiply (-5 + k) * (-8 + 3k) (-5(-8 + 3k) + k(-8 + 3k)) = 0 ((-8 * -5 + 3k * -5) + k(-8 + 3k)) = 0 ((40 + -15k) + k(-8 + 3k)) = 0 (40 + -15k + (-8 * k + 3k * k)) = 0 (40 + -15k + (-8k + 3k2)) = 0 Combine like terms: -15k + -8k = -23k (40 + -23k + 3k2) = 0 Solving 40 + -23k + 3k2 = 0 Solving for variable 'k'. Factor a trinomial. (8 + -3k)(5 + -1k) = 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 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 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 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Solution
k = {2.666666667, 5}
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