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Simplifying (4k + 3)(k + 7) = 0 Reorder the terms: (3 + 4k)(k + 7) = 0 Reorder the terms: (3 + 4k)(7 + k) = 0 Multiply (3 + 4k) * (7 + k) (3(7 + k) + 4k * (7 + k)) = 0 ((7 * 3 + k * 3) + 4k * (7 + k)) = 0 ((21 + 3k) + 4k * (7 + k)) = 0 (21 + 3k + (7 * 4k + k * 4k)) = 0 (21 + 3k + (28k + 4k2)) = 0 Combine like terms: 3k + 28k = 31k (21 + 31k + 4k2) = 0 Solving 21 + 31k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + k)(3 + 4k) = 0Subproblem 1
Set the factor '(7 + k)' equal to zero and attempt to solve: Simplifying 7 + k = 0 Solving 7 + k = 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 + k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + k = 0 + -7 k = 0 + -7 Combine like terms: 0 + -7 = -7 k = -7 Simplifying k = -7Subproblem 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 = {-7, -0.75}
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