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Simplifying (3k + -2)(k + 12) = 0 Reorder the terms: (-2 + 3k)(k + 12) = 0 Reorder the terms: (-2 + 3k)(12 + k) = 0 Multiply (-2 + 3k) * (12 + k) (-2(12 + k) + 3k * (12 + k)) = 0 ((12 * -2 + k * -2) + 3k * (12 + k)) = 0 ((-24 + -2k) + 3k * (12 + k)) = 0 (-24 + -2k + (12 * 3k + k * 3k)) = 0 (-24 + -2k + (36k + 3k2)) = 0 Combine like terms: -2k + 36k = 34k (-24 + 34k + 3k2) = 0 Solving -24 + 34k + 3k2 = 0 Solving for variable 'k'. Factor a trinomial. (-12 + -1k)(2 + -3k) = 0Subproblem 1
Set the factor '(-12 + -1k)' equal to zero and attempt to solve: Simplifying -12 + -1k = 0 Solving -12 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1k = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1k = 0 + 12 -1k = 0 + 12 Combine like terms: 0 + 12 = 12 -1k = 12 Divide each side by '-1'. k = -12 Simplifying k = -12Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 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 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Solution
k = {-12, 0.6666666667}
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