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Simplifying (2k + 4)(k + -3) = 0 Reorder the terms: (4 + 2k)(k + -3) = 0 Reorder the terms: (4 + 2k)(-3 + k) = 0 Multiply (4 + 2k) * (-3 + k) (4(-3 + k) + 2k * (-3 + k)) = 0 ((-3 * 4 + k * 4) + 2k * (-3 + k)) = 0 ((-12 + 4k) + 2k * (-3 + k)) = 0 (-12 + 4k + (-3 * 2k + k * 2k)) = 0 (-12 + 4k + (-6k + 2k2)) = 0 Combine like terms: 4k + -6k = -2k (-12 + -2k + 2k2) = 0 Solving -12 + -2k + 2k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -1k + k2) = 0 Factor a trinomial. 2((-2 + -1k)(3 + -1k)) = 0 Ignore the factor 2.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 '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {-2, 3}
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