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Simplifying (6k + 5)(7k + 4) = 0 Reorder the terms: (5 + 6k)(7k + 4) = 0 Reorder the terms: (5 + 6k)(4 + 7k) = 0 Multiply (5 + 6k) * (4 + 7k) (5(4 + 7k) + 6k * (4 + 7k)) = 0 ((4 * 5 + 7k * 5) + 6k * (4 + 7k)) = 0 ((20 + 35k) + 6k * (4 + 7k)) = 0 (20 + 35k + (4 * 6k + 7k * 6k)) = 0 (20 + 35k + (24k + 42k2)) = 0 Combine like terms: 35k + 24k = 59k (20 + 59k + 42k2) = 0 Solving 20 + 59k + 42k2 = 0 Solving for variable 'k'. Factor a trinomial. (5 + 6k)(4 + 7k) = 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 '(4 + 7k)' equal to zero and attempt to solve: Simplifying 4 + 7k = 0 Solving 4 + 7k = 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 + 7k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7k = 0 + -4 7k = 0 + -4 Combine like terms: 0 + -4 = -4 7k = -4 Divide each side by '7'. k = -0.5714285714 Simplifying k = -0.5714285714Solution
k = {-0.8333333333, -0.5714285714}
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