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Simplifying 2k(k + 3) = (3k + 1)(k + 3) Reorder the terms: 2k(3 + k) = (3k + 1)(k + 3) (3 * 2k + k * 2k) = (3k + 1)(k + 3) (6k + 2k2) = (3k + 1)(k + 3) Reorder the terms: 6k + 2k2 = (1 + 3k)(k + 3) Reorder the terms: 6k + 2k2 = (1 + 3k)(3 + k) Multiply (1 + 3k) * (3 + k) 6k + 2k2 = (1(3 + k) + 3k * (3 + k)) 6k + 2k2 = ((3 * 1 + k * 1) + 3k * (3 + k)) 6k + 2k2 = ((3 + 1k) + 3k * (3 + k)) 6k + 2k2 = (3 + 1k + (3 * 3k + k * 3k)) 6k + 2k2 = (3 + 1k + (9k + 3k2)) Combine like terms: 1k + 9k = 10k 6k + 2k2 = (3 + 10k + 3k2) Solving 6k + 2k2 = 3 + 10k + 3k2 Solving for variable 'k'. Reorder the terms: -3 + 6k + -10k + 2k2 + -3k2 = 3 + 10k + 3k2 + -3 + -10k + -3k2 Combine like terms: 6k + -10k = -4k -3 + -4k + 2k2 + -3k2 = 3 + 10k + 3k2 + -3 + -10k + -3k2 Combine like terms: 2k2 + -3k2 = -1k2 -3 + -4k + -1k2 = 3 + 10k + 3k2 + -3 + -10k + -3k2 Reorder the terms: -3 + -4k + -1k2 = 3 + -3 + 10k + -10k + 3k2 + -3k2 Combine like terms: 3 + -3 = 0 -3 + -4k + -1k2 = 0 + 10k + -10k + 3k2 + -3k2 -3 + -4k + -1k2 = 10k + -10k + 3k2 + -3k2 Combine like terms: 10k + -10k = 0 -3 + -4k + -1k2 = 0 + 3k2 + -3k2 -3 + -4k + -1k2 = 3k2 + -3k2 Combine like terms: 3k2 + -3k2 = 0 -3 + -4k + -1k2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 4k + k2) = 0 Factor a trinomial. -1((3 + k)(1 + k)) = 0 Ignore the factor -1.Subproblem 1
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 = -3Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 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 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Solution
k = {-3, -1}
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