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Simplifying 2(k + -2)(k + 6) = 0 Reorder the terms: 2(-2 + k)(k + 6) = 0 Reorder the terms: 2(-2 + k)(6 + k) = 0 Multiply (-2 + k) * (6 + k) 2(-2(6 + k) + k(6 + k)) = 0 2((6 * -2 + k * -2) + k(6 + k)) = 0 2((-12 + -2k) + k(6 + k)) = 0 2(-12 + -2k + (6 * k + k * k)) = 0 2(-12 + -2k + (6k + k2)) = 0 Combine like terms: -2k + 6k = 4k 2(-12 + 4k + k2) = 0 (-12 * 2 + 4k * 2 + k2 * 2) = 0 (-24 + 8k + 2k2) = 0 Solving -24 + 8k + 2k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 4k + k2) = 0 Factor a trinomial. 2((-6 + -1k)(2 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve: Simplifying -6 + -1k = 0 Solving -6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1k = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1k = 0 + 6 -1k = 0 + 6 Combine like terms: 0 + 6 = 6 -1k = 6 Divide each side by '-1'. k = -6 Simplifying k = -6Subproblem 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 = {-6, 2}
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