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Simplifying (2k + 4)(4k + 2) = 0 Reorder the terms: (4 + 2k)(4k + 2) = 0 Reorder the terms: (4 + 2k)(2 + 4k) = 0 Multiply (4 + 2k) * (2 + 4k) (4(2 + 4k) + 2k * (2 + 4k)) = 0 ((2 * 4 + 4k * 4) + 2k * (2 + 4k)) = 0 ((8 + 16k) + 2k * (2 + 4k)) = 0 (8 + 16k + (2 * 2k + 4k * 2k)) = 0 (8 + 16k + (4k + 8k2)) = 0 Combine like terms: 16k + 4k = 20k (8 + 20k + 8k2) = 0 Solving 8 + 20k + 8k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 5k + 2k2) = 0 Factor a trinomial. 4((2 + k)(1 + 2k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + k)' equal to zero and attempt to solve: Simplifying 2 + k = 0 Solving 2 + k = 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 + k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k = 0 + -2 k = 0 + -2 Combine like terms: 0 + -2 = -2 k = -2 Simplifying k = -2Subproblem 2
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 = -0.5Solution
k = {-2, -0.5}
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