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Simplifying (5k + 7)(k + 2) = 0 Reorder the terms: (7 + 5k)(k + 2) = 0 Reorder the terms: (7 + 5k)(2 + k) = 0 Multiply (7 + 5k) * (2 + k) (7(2 + k) + 5k * (2 + k)) = 0 ((2 * 7 + k * 7) + 5k * (2 + k)) = 0 ((14 + 7k) + 5k * (2 + k)) = 0 (14 + 7k + (2 * 5k + k * 5k)) = 0 (14 + 7k + (10k + 5k2)) = 0 Combine like terms: 7k + 10k = 17k (14 + 17k + 5k2) = 0 Solving 14 + 17k + 5k2 = 0 Solving for variable 'k'. Factor a trinomial. (2 + k)(7 + 5k) = 0Subproblem 1
Set the factor '(2 + k)' equal to zero and attempt to solve: Simplifying 2 + k = 0 Solving 2 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k = 0 + -2 k = 0 + -2 Combine like terms: 0 + -2 = -2 k = -2 Simplifying k = -2Subproblem 2
Set the factor '(7 + 5k)' equal to zero and attempt to solve: Simplifying 7 + 5k = 0 Solving 7 + 5k = 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 + 5k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5k = 0 + -7 5k = 0 + -7 Combine like terms: 0 + -7 = -7 5k = -7 Divide each side by '5'. k = -1.4 Simplifying k = -1.4Solution
k = {-2, -1.4}
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