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Simplifying (3k + 4)(9k + 5) = 0 Reorder the terms: (4 + 3k)(9k + 5) = 0 Reorder the terms: (4 + 3k)(5 + 9k) = 0 Multiply (4 + 3k) * (5 + 9k) (4(5 + 9k) + 3k * (5 + 9k)) = 0 ((5 * 4 + 9k * 4) + 3k * (5 + 9k)) = 0 ((20 + 36k) + 3k * (5 + 9k)) = 0 (20 + 36k + (5 * 3k + 9k * 3k)) = 0 (20 + 36k + (15k + 27k2)) = 0 Combine like terms: 36k + 15k = 51k (20 + 51k + 27k2) = 0 Solving 20 + 51k + 27k2 = 0 Solving for variable 'k'. Factor a trinomial. (4 + 3k)(5 + 9k) = 0Subproblem 1
Set the factor '(4 + 3k)' equal to zero and attempt to solve: Simplifying 4 + 3k = 0 Solving 4 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3k = 0 + -4 3k = 0 + -4 Combine like terms: 0 + -4 = -4 3k = -4 Divide each side by '3'. k = -1.333333333 Simplifying k = -1.333333333Subproblem 2
Set the factor '(5 + 9k)' equal to zero and attempt to solve: Simplifying 5 + 9k = 0 Solving 5 + 9k = 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 + 9k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9k = 0 + -5 9k = 0 + -5 Combine like terms: 0 + -5 = -5 9k = -5 Divide each side by '9'. k = -0.5555555556 Simplifying k = -0.5555555556Solution
k = {-1.333333333, -0.5555555556}
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