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Simplifying 6k * k + -30k + -84 = 0 Multiply k * k 6k2 + -30k + -84 = 0 Reorder the terms: -84 + -30k + 6k2 = 0 Solving -84 + -30k + 6k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + -5k + k2) = 0 Factor a trinomial. 6((-2 + -1k)(7 + -1k)) = 0 Ignore the factor 6.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 '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {-2, 7}
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