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Simplifying 2k2 = 10k + -12 Reorder the terms: 2k2 = -12 + 10k Solving 2k2 = -12 + 10k Solving for variable 'k'. Reorder the terms: 12 + -10k + 2k2 = -12 + 10k + 12 + -10k Reorder the terms: 12 + -10k + 2k2 = -12 + 12 + 10k + -10k Combine like terms: -12 + 12 = 0 12 + -10k + 2k2 = 0 + 10k + -10k 12 + -10k + 2k2 = 10k + -10k Combine like terms: 10k + -10k = 0 12 + -10k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -5k + k2) = 0 Factor a trinomial. 2((2 + -1k)(3 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 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 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Subproblem 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 = {2, 3}
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