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Simplifying 50n2 + 315n + 405 = 0 Reorder the terms: 405 + 315n + 50n2 = 0 Solving 405 + 315n + 50n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(81 + 63n + 10n2) = 0 Factor a trinomial. 5((9 + 2n)(9 + 5n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + 2n)' equal to zero and attempt to solve: Simplifying 9 + 2n = 0 Solving 9 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2n = 0 + -9 2n = 0 + -9 Combine like terms: 0 + -9 = -9 2n = -9 Divide each side by '2'. n = -4.5 Simplifying n = -4.5Subproblem 2
Set the factor '(9 + 5n)' equal to zero and attempt to solve: Simplifying 9 + 5n = 0 Solving 9 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5n = 0 + -9 5n = 0 + -9 Combine like terms: 0 + -9 = -9 5n = -9 Divide each side by '5'. n = -1.8 Simplifying n = -1.8Solution
n = {-4.5, -1.8}
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