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Simplifying 6k2 + 12k + -40 = 8 Reorder the terms: -40 + 12k + 6k2 = 8 Solving -40 + 12k + 6k2 = 8 Solving for variable 'k'. Reorder the terms: -40 + -8 + 12k + 6k2 = 8 + -8 Combine like terms: -40 + -8 = -48 -48 + 12k + 6k2 = 8 + -8 Combine like terms: 8 + -8 = 0 -48 + 12k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + 2k + k2) = 0 Factor a trinomial. 6((-4 + -1k)(2 + -1k)) = 0 Ignore the factor 6.Subproblem 1
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 = -4Subproblem 2
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 = 2Solution
k = {-4, 2}
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