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Simplifying (4k + 5)(k + 7) = 0 Reorder the terms: (5 + 4k)(k + 7) = 0 Reorder the terms: (5 + 4k)(7 + k) = 0 Multiply (5 + 4k) * (7 + k) (5(7 + k) + 4k * (7 + k)) = 0 ((7 * 5 + k * 5) + 4k * (7 + k)) = 0 ((35 + 5k) + 4k * (7 + k)) = 0 (35 + 5k + (7 * 4k + k * 4k)) = 0 (35 + 5k + (28k + 4k2)) = 0 Combine like terms: 5k + 28k = 33k (35 + 33k + 4k2) = 0 Solving 35 + 33k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + k)(5 + 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 '(5 + 4k)' equal to zero and attempt to solve: Simplifying 5 + 4k = 0 Solving 5 + 4k = 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 + 4k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4k = 0 + -5 4k = 0 + -5 Combine like terms: 0 + -5 = -5 4k = -5 Divide each side by '4'. k = -1.25 Simplifying k = -1.25Solution
k = {-7, -1.25}
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