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Simplifying (k + -4)(k + -5) = 0 Reorder the terms: (-4 + k)(k + -5) = 0 Reorder the terms: (-4 + k)(-5 + k) = 0 Multiply (-4 + k) * (-5 + k) (-4(-5 + k) + k(-5 + k)) = 0 ((-5 * -4 + k * -4) + k(-5 + k)) = 0 ((20 + -4k) + k(-5 + k)) = 0 (20 + -4k + (-5 * k + k * k)) = 0 (20 + -4k + (-5k + k2)) = 0 Combine like terms: -4k + -5k = -9k (20 + -9k + k2) = 0 Solving 20 + -9k + k2 = 0 Solving for variable 'k'. Factor a trinomial. (4 + -1k)(5 + -1k) = 0Subproblem 1
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Subproblem 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 = {4, 5}
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