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Simplifying 6k2 = -12k + 18 Reorder the terms: 6k2 = 18 + -12k Solving 6k2 = 18 + -12k Solving for variable 'k'. Reorder the terms: -18 + 12k + 6k2 = 18 + -12k + -18 + 12k Reorder the terms: -18 + 12k + 6k2 = 18 + -18 + -12k + 12k Combine like terms: 18 + -18 = 0 -18 + 12k + 6k2 = 0 + -12k + 12k -18 + 12k + 6k2 = -12k + 12k Combine like terms: -12k + 12k = 0 -18 + 12k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 2k + k2) = 0 Factor a trinomial. 6((-3 + -1k)(1 + -1k)) = 0 Ignore the factor 6.Subproblem 1
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 = -3Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 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 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Solution
k = {-3, 1}
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