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Simplifying (4k + -5)(4k + -6) = 0 Reorder the terms: (-5 + 4k)(4k + -6) = 0 Reorder the terms: (-5 + 4k)(-6 + 4k) = 0 Multiply (-5 + 4k) * (-6 + 4k) (-5(-6 + 4k) + 4k * (-6 + 4k)) = 0 ((-6 * -5 + 4k * -5) + 4k * (-6 + 4k)) = 0 ((30 + -20k) + 4k * (-6 + 4k)) = 0 (30 + -20k + (-6 * 4k + 4k * 4k)) = 0 (30 + -20k + (-24k + 16k2)) = 0 Combine like terms: -20k + -24k = -44k (30 + -44k + 16k2) = 0 Solving 30 + -44k + 16k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -22k + 8k2) = 0 Factor a trinomial. 2((5 + -4k)(3 + -2k)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.25Subproblem 2
Set the factor '(3 + -2k)' equal to zero and attempt to solve: Simplifying 3 + -2k = 0 Solving 3 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2k = 0 + -3 -2k = 0 + -3 Combine like terms: 0 + -3 = -3 -2k = -3 Divide each side by '-2'. k = 1.5 Simplifying k = 1.5Solution
k = {1.25, 1.5}
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