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Simplifying (k + 3)(4k + 7) = 0 Reorder the terms: (3 + k)(4k + 7) = 0 Reorder the terms: (3 + k)(7 + 4k) = 0 Multiply (3 + k) * (7 + 4k) (3(7 + 4k) + k(7 + 4k)) = 0 ((7 * 3 + 4k * 3) + k(7 + 4k)) = 0 ((21 + 12k) + k(7 + 4k)) = 0 (21 + 12k + (7 * k + 4k * k)) = 0 (21 + 12k + (7k + 4k2)) = 0 Combine like terms: 12k + 7k = 19k (21 + 19k + 4k2) = 0 Solving 21 + 19k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (3 + k)(7 + 4k) = 0Subproblem 1
Set the factor '(3 + k)' equal to zero and attempt to solve: Simplifying 3 + k = 0 Solving 3 + k = 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 + k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + k = 0 + -3 k = 0 + -3 Combine like terms: 0 + -3 = -3 k = -3 Simplifying k = -3Subproblem 2
Set the factor '(7 + 4k)' equal to zero and attempt to solve: Simplifying 7 + 4k = 0 Solving 7 + 4k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4k = 0 + -7 4k = 0 + -7 Combine like terms: 0 + -7 = -7 4k = -7 Divide each side by '4'. k = -1.75 Simplifying k = -1.75Solution
k = {-3, -1.75}
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