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Simplifying (5k + -4)(8k + -6) = 0 Reorder the terms: (-4 + 5k)(8k + -6) = 0 Reorder the terms: (-4 + 5k)(-6 + 8k) = 0 Multiply (-4 + 5k) * (-6 + 8k) (-4(-6 + 8k) + 5k * (-6 + 8k)) = 0 ((-6 * -4 + 8k * -4) + 5k * (-6 + 8k)) = 0 ((24 + -32k) + 5k * (-6 + 8k)) = 0 (24 + -32k + (-6 * 5k + 8k * 5k)) = 0 (24 + -32k + (-30k + 40k2)) = 0 Combine like terms: -32k + -30k = -62k (24 + -62k + 40k2) = 0 Solving 24 + -62k + 40k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -31k + 20k2) = 0 Factor a trinomial. 2((3 + -4k)(4 + -5k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4k)' equal to zero and attempt to solve: Simplifying 3 + -4k = 0 Solving 3 + -4k = 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 + -4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4k = 0 + -3 -4k = 0 + -3 Combine like terms: 0 + -3 = -3 -4k = -3 Divide each side by '-4'. k = 0.75 Simplifying k = 0.75Subproblem 2
Set the factor '(4 + -5k)' equal to zero and attempt to solve: Simplifying 4 + -5k = 0 Solving 4 + -5k = 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 + -5k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5k = 0 + -4 -5k = 0 + -4 Combine like terms: 0 + -4 = -4 -5k = -4 Divide each side by '-5'. k = 0.8 Simplifying k = 0.8Solution
k = {0.75, 0.8}
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