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Simplifying (4k + 9)(5k + 7) = 0 Reorder the terms: (9 + 4k)(5k + 7) = 0 Reorder the terms: (9 + 4k)(7 + 5k) = 0 Multiply (9 + 4k) * (7 + 5k) (9(7 + 5k) + 4k * (7 + 5k)) = 0 ((7 * 9 + 5k * 9) + 4k * (7 + 5k)) = 0 ((63 + 45k) + 4k * (7 + 5k)) = 0 (63 + 45k + (7 * 4k + 5k * 4k)) = 0 (63 + 45k + (28k + 20k2)) = 0 Combine like terms: 45k + 28k = 73k (63 + 73k + 20k2) = 0 Solving 63 + 73k + 20k2 = 0 Solving for variable 'k'. Factor a trinomial. (9 + 4k)(7 + 5k) = 0Subproblem 1
Set the factor '(9 + 4k)' equal to zero and attempt to solve: Simplifying 9 + 4k = 0 Solving 9 + 4k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4k = 0 + -9 4k = 0 + -9 Combine like terms: 0 + -9 = -9 4k = -9 Divide each side by '4'. k = -2.25 Simplifying k = -2.25Subproblem 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 = {-2.25, -1.4}
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