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Simplifying (3k + -1)(6k + 5) = 0 Reorder the terms: (-1 + 3k)(6k + 5) = 0 Reorder the terms: (-1 + 3k)(5 + 6k) = 0 Multiply (-1 + 3k) * (5 + 6k) (-1(5 + 6k) + 3k * (5 + 6k)) = 0 ((5 * -1 + 6k * -1) + 3k * (5 + 6k)) = 0 ((-5 + -6k) + 3k * (5 + 6k)) = 0 (-5 + -6k + (5 * 3k + 6k * 3k)) = 0 (-5 + -6k + (15k + 18k2)) = 0 Combine like terms: -6k + 15k = 9k (-5 + 9k + 18k2) = 0 Solving -5 + 9k + 18k2 = 0 Solving for variable 'k'. Factor a trinomial. (-5 + -6k)(1 + -3k) = 0Subproblem 1
Set the factor '(-5 + -6k)' equal to zero and attempt to solve: Simplifying -5 + -6k = 0 Solving -5 + -6k = 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 + -6k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6k = 0 + 5 -6k = 0 + 5 Combine like terms: 0 + 5 = 5 -6k = 5 Divide each side by '-6'. k = -0.8333333333 Simplifying k = -0.8333333333Subproblem 2
Set the factor '(1 + -3k)' equal to zero and attempt to solve: Simplifying 1 + -3k = 0 Solving 1 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3k = 0 + -1 -3k = 0 + -1 Combine like terms: 0 + -1 = -1 -3k = -1 Divide each side by '-3'. k = 0.3333333333 Simplifying k = 0.3333333333Solution
k = {-0.8333333333, 0.3333333333}
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