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Simplifying k(3k + 2) = k(5k + -4) Reorder the terms: k(2 + 3k) = k(5k + -4) (2 * k + 3k * k) = k(5k + -4) (2k + 3k2) = k(5k + -4) Reorder the terms: 2k + 3k2 = k(-4 + 5k) 2k + 3k2 = (-4 * k + 5k * k) 2k + 3k2 = (-4k + 5k2) Solving 2k + 3k2 = -4k + 5k2 Solving for variable 'k'. Reorder the terms: 2k + 4k + 3k2 + -5k2 = -4k + 5k2 + 4k + -5k2 Combine like terms: 2k + 4k = 6k 6k + 3k2 + -5k2 = -4k + 5k2 + 4k + -5k2 Combine like terms: 3k2 + -5k2 = -2k2 6k + -2k2 = -4k + 5k2 + 4k + -5k2 Reorder the terms: 6k + -2k2 = -4k + 4k + 5k2 + -5k2 Combine like terms: -4k + 4k = 0 6k + -2k2 = 0 + 5k2 + -5k2 6k + -2k2 = 5k2 + -5k2 Combine like terms: 5k2 + -5k2 = 0 6k + -2k2 = 0 Factor out the Greatest Common Factor (GCF), '2k'. 2k(3 + -1k) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 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 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {0, 3}
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