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Simplifying 6(k2 + -7k + 12) = 0 Reorder the terms: 6(12 + -7k + k2) = 0 (12 * 6 + -7k * 6 + k2 * 6) = 0 (72 + -42k + 6k2) = 0 Solving 72 + -42k + 6k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(12 + -7k + k2) = 0 Factor a trinomial. 6((3 + -1k)(4 + -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 '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {3, 4}
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