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Simplifying (k + 4)(3k + -8) = 0 Reorder the terms: (4 + k)(3k + -8) = 0 Reorder the terms: (4 + k)(-8 + 3k) = 0 Multiply (4 + k) * (-8 + 3k) (4(-8 + 3k) + k(-8 + 3k)) = 0 ((-8 * 4 + 3k * 4) + k(-8 + 3k)) = 0 ((-32 + 12k) + k(-8 + 3k)) = 0 (-32 + 12k + (-8 * k + 3k * k)) = 0 (-32 + 12k + (-8k + 3k2)) = 0 Combine like terms: 12k + -8k = 4k (-32 + 4k + 3k2) = 0 Solving -32 + 4k + 3k2 = 0 Solving for variable 'k'. Factor a trinomial. (-4 + -1k)(8 + -3k) = 0Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve: Simplifying -4 + -1k = 0 Solving -4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1k = 0 + 4 -1k = 0 + 4 Combine like terms: 0 + 4 = 4 -1k = 4 Divide each side by '-1'. k = -4 Simplifying k = -4Subproblem 2
Set the factor '(8 + -3k)' equal to zero and attempt to solve: Simplifying 8 + -3k = 0 Solving 8 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3k = 0 + -8 -3k = 0 + -8 Combine like terms: 0 + -8 = -8 -3k = -8 Divide each side by '-3'. k = 2.666666667 Simplifying k = 2.666666667Solution
k = {-4, 2.666666667}
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