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Simplifying -125n2 + 4125n + -32500 = 0 Reorder the terms: -32500 + 4125n + -125n2 = 0 Solving -32500 + 4125n + -125n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '125'. 125(-260 + 33n + -1n2) = 0 Factor a trinomial. 125((-20 + n)(13 + -1n)) = 0 Ignore the factor 125.Subproblem 1
Set the factor '(-20 + n)' equal to zero and attempt to solve: Simplifying -20 + n = 0 Solving -20 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + n = 0 + 20 Combine like terms: -20 + 20 = 0 0 + n = 0 + 20 n = 0 + 20 Combine like terms: 0 + 20 = 20 n = 20 Simplifying n = 20Subproblem 2
Set the factor '(13 + -1n)' equal to zero and attempt to solve: Simplifying 13 + -1n = 0 Solving 13 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n = 0 + -13 -1n = 0 + -13 Combine like terms: 0 + -13 = -13 -1n = -13 Divide each side by '-1'. n = 13 Simplifying n = 13Solution
n = {20, 13}
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