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Simplifying 6k2 + -18k + -18 = 6 Reorder the terms: -18 + -18k + 6k2 = 6 Solving -18 + -18k + 6k2 = 6 Solving for variable 'k'. Reorder the terms: -18 + -6 + -18k + 6k2 = 6 + -6 Combine like terms: -18 + -6 = -24 -24 + -18k + 6k2 = 6 + -6 Combine like terms: 6 + -6 = 0 -24 + -18k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -3k + k2) = 0 Factor a trinomial. 6((-1 + -1k)(4 + -1k)) = 0 Ignore the factor 6.Subproblem 1
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 = -1Subproblem 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 = {-1, 4}
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