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Simplifying (6n + 3)(5n + 4) = 0 Reorder the terms: (3 + 6n)(5n + 4) = 0 Reorder the terms: (3 + 6n)(4 + 5n) = 0 Multiply (3 + 6n) * (4 + 5n) (3(4 + 5n) + 6n * (4 + 5n)) = 0 ((4 * 3 + 5n * 3) + 6n * (4 + 5n)) = 0 ((12 + 15n) + 6n * (4 + 5n)) = 0 (12 + 15n + (4 * 6n + 5n * 6n)) = 0 (12 + 15n + (24n + 30n2)) = 0 Combine like terms: 15n + 24n = 39n (12 + 39n + 30n2) = 0 Solving 12 + 39n + 30n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 13n + 10n2) = 0 Factor a trinomial. 3((4 + 5n)(1 + 2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 5n)' equal to zero and attempt to solve: Simplifying 4 + 5n = 0 Solving 4 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n = 0 + -4 5n = 0 + -4 Combine like terms: 0 + -4 = -4 5n = -4 Divide each side by '5'. n = -0.8 Simplifying n = -0.8Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-0.8, -0.5}
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