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Simplifying (4k + -5)(3k + -2) = 0 Reorder the terms: (-5 + 4k)(3k + -2) = 0 Reorder the terms: (-5 + 4k)(-2 + 3k) = 0 Multiply (-5 + 4k) * (-2 + 3k) (-5(-2 + 3k) + 4k * (-2 + 3k)) = 0 ((-2 * -5 + 3k * -5) + 4k * (-2 + 3k)) = 0 ((10 + -15k) + 4k * (-2 + 3k)) = 0 (10 + -15k + (-2 * 4k + 3k * 4k)) = 0 (10 + -15k + (-8k + 12k2)) = 0 Combine like terms: -15k + -8k = -23k (10 + -23k + 12k2) = 0 Solving 10 + -23k + 12k2 = 0 Solving for variable 'k'. Factor a trinomial. (2 + -3k)(5 + -4k) = 0Subproblem 1
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 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 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Subproblem 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 = {0.6666666667, 1.25}
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