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Simplifying (6k + 1)(4k + 2) = 0 Reorder the terms: (1 + 6k)(4k + 2) = 0 Reorder the terms: (1 + 6k)(2 + 4k) = 0 Multiply (1 + 6k) * (2 + 4k) (1(2 + 4k) + 6k * (2 + 4k)) = 0 ((2 * 1 + 4k * 1) + 6k * (2 + 4k)) = 0 ((2 + 4k) + 6k * (2 + 4k)) = 0 (2 + 4k + (2 * 6k + 4k * 6k)) = 0 (2 + 4k + (12k + 24k2)) = 0 Combine like terms: 4k + 12k = 16k (2 + 16k + 24k2) = 0 Solving 2 + 16k + 24k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 8k + 12k2) = 0 Factor a trinomial. 2((1 + 2k)(1 + 6k)) = 0 Ignore the factor 2.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 '(1 + 6k)' equal to zero and attempt to solve: Simplifying 1 + 6k = 0 Solving 1 + 6k = 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 + 6k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6k = 0 + -1 6k = 0 + -1 Combine like terms: 0 + -1 = -1 6k = -1 Divide each side by '6'. k = -0.1666666667 Simplifying k = -0.1666666667Solution
k = {-0.5, -0.1666666667}
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