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Simplifying (3 + 7k)(5 + 2k) = 0 Multiply (3 + 7k) * (5 + 2k) (3(5 + 2k) + 7k * (5 + 2k)) = 0 ((5 * 3 + 2k * 3) + 7k * (5 + 2k)) = 0 ((15 + 6k) + 7k * (5 + 2k)) = 0 (15 + 6k + (5 * 7k + 2k * 7k)) = 0 (15 + 6k + (35k + 14k2)) = 0 Combine like terms: 6k + 35k = 41k (15 + 41k + 14k2) = 0 Solving 15 + 41k + 14k2 = 0 Solving for variable 'k'. Factor a trinomial. (5 + 2k)(3 + 7k) = 0Subproblem 1
Set the factor '(5 + 2k)' equal to zero and attempt to solve: Simplifying 5 + 2k = 0 Solving 5 + 2k = 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 + 2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2k = 0 + -5 2k = 0 + -5 Combine like terms: 0 + -5 = -5 2k = -5 Divide each side by '2'. k = -2.5 Simplifying k = -2.5Subproblem 2
Set the factor '(3 + 7k)' equal to zero and attempt to solve: Simplifying 3 + 7k = 0 Solving 3 + 7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 7k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7k = 0 + -3 7k = 0 + -3 Combine like terms: 0 + -3 = -3 7k = -3 Divide each side by '7'. k = -0.4285714286 Simplifying k = -0.4285714286Solution
k = {-2.5, -0.4285714286}
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