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Simplifying (4k + 3)(k + 5) = 0 Reorder the terms: (3 + 4k)(k + 5) = 0 Reorder the terms: (3 + 4k)(5 + k) = 0 Multiply (3 + 4k) * (5 + k) (3(5 + k) + 4k * (5 + k)) = 0 ((5 * 3 + k * 3) + 4k * (5 + k)) = 0 ((15 + 3k) + 4k * (5 + k)) = 0 (15 + 3k + (5 * 4k + k * 4k)) = 0 (15 + 3k + (20k + 4k2)) = 0 Combine like terms: 3k + 20k = 23k (15 + 23k + 4k2) = 0 Solving 15 + 23k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (5 + k)(3 + 4k) = 0Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve: Simplifying 5 + k = 0 Solving 5 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5Subproblem 2
Set the factor '(3 + 4k)' equal to zero and attempt to solve: Simplifying 3 + 4k = 0 Solving 3 + 4k = 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 + 4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4k = 0 + -3 4k = 0 + -3 Combine like terms: 0 + -3 = -3 4k = -3 Divide each side by '4'. k = -0.75 Simplifying k = -0.75Solution
k = {-5, -0.75}
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