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Simplifying (6k + 5)(5k + 5) = 0 Reorder the terms: (5 + 6k)(5k + 5) = 0 Reorder the terms: (5 + 6k)(5 + 5k) = 0 Multiply (5 + 6k) * (5 + 5k) (5(5 + 5k) + 6k * (5 + 5k)) = 0 ((5 * 5 + 5k * 5) + 6k * (5 + 5k)) = 0 ((25 + 25k) + 6k * (5 + 5k)) = 0 (25 + 25k + (5 * 6k + 5k * 6k)) = 0 (25 + 25k + (30k + 30k2)) = 0 Combine like terms: 25k + 30k = 55k (25 + 55k + 30k2) = 0 Solving 25 + 55k + 30k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + 11k + 6k2) = 0 Factor a trinomial. 5((1 + k)(5 + 6k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 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 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Subproblem 2
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 = -0.8333333333Solution
k = {-1, -0.8333333333}
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