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Simplifying (2k + 6)(-4k + 5) = 0 Reorder the terms: (6 + 2k)(-4k + 5) = 0 Reorder the terms: (6 + 2k)(5 + -4k) = 0 Multiply (6 + 2k) * (5 + -4k) (6(5 + -4k) + 2k * (5 + -4k)) = 0 ((5 * 6 + -4k * 6) + 2k * (5 + -4k)) = 0 ((30 + -24k) + 2k * (5 + -4k)) = 0 (30 + -24k + (5 * 2k + -4k * 2k)) = 0 (30 + -24k + (10k + -8k2)) = 0 Combine like terms: -24k + 10k = -14k (30 + -14k + -8k2) = 0 Solving 30 + -14k + -8k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -7k + -4k2) = 0 Factor a trinomial. 2((5 + -4k)(3 + k)) = 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 + k)' equal to zero and attempt to solve: Simplifying 3 + k = 0 Solving 3 + k = 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 + k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + k = 0 + -3 k = 0 + -3 Combine like terms: 0 + -3 = -3 k = -3 Simplifying k = -3Solution
k = {1.25, -3}
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