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Simplifying 3k2 + -21k + 3k + -21 = 0 Reorder the terms: -21 + -21k + 3k + 3k2 = 0 Combine like terms: -21k + 3k = -18k -21 + -18k + 3k2 = 0 Solving -21 + -18k + 3k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -6k + k2) = 0 Factor a trinomial. 3((-1 + -1k)(7 + -1k)) = 0 Ignore the factor 3.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 '(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 = {-1, 7}
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