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Simplifying 4n * n + 10n + -15000 = 0 Multiply n * n 4n2 + 10n + -15000 = 0 Reorder the terms: -15000 + 10n + 4n2 = 0 Solving -15000 + 10n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7500 + 5n + 2n2) = 0 Factor a trinomial. 2((-125 + -2n)(60 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-125 + -2n)' equal to zero and attempt to solve: Simplifying -125 + -2n = 0 Solving -125 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + -2n = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -2n = 0 + 125 -2n = 0 + 125 Combine like terms: 0 + 125 = 125 -2n = 125 Divide each side by '-2'. n = -62.5 Simplifying n = -62.5Subproblem 2
Set the factor '(60 + -1n)' equal to zero and attempt to solve: Simplifying 60 + -1n = 0 Solving 60 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1n = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1n = 0 + -60 -1n = 0 + -60 Combine like terms: 0 + -60 = -60 -1n = -60 Divide each side by '-1'. n = 60 Simplifying n = 60Solution
n = {-62.5, 60}
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