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Simplifying (4k + -2)(8k + -6) = 0 Reorder the terms: (-2 + 4k)(8k + -6) = 0 Reorder the terms: (-2 + 4k)(-6 + 8k) = 0 Multiply (-2 + 4k) * (-6 + 8k) (-2(-6 + 8k) + 4k * (-6 + 8k)) = 0 ((-6 * -2 + 8k * -2) + 4k * (-6 + 8k)) = 0 ((12 + -16k) + 4k * (-6 + 8k)) = 0 (12 + -16k + (-6 * 4k + 8k * 4k)) = 0 (12 + -16k + (-24k + 32k2)) = 0 Combine like terms: -16k + -24k = -40k (12 + -40k + 32k2) = 0 Solving 12 + -40k + 32k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -10k + 8k2) = 0 Factor a trinomial. 4((1 + -2k)(3 + -4k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2k)' equal to zero and attempt to solve: Simplifying 1 + -2k = 0 Solving 1 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k = 0 + -1 -2k = 0 + -1 Combine like terms: 0 + -1 = -1 -2k = -1 Divide each side by '-2'. k = 0.5 Simplifying k = 0.5Subproblem 2
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 = 0.75Solution
k = {0.5, 0.75}
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