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Simplifying 5n2 + -10n = 75 Reorder the terms: -10n + 5n2 = 75 Solving -10n + 5n2 = 75 Solving for variable 'n'. Reorder the terms: -75 + -10n + 5n2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -10n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + -2n + n2) = 0 Factor a trinomial. 5((-3 + -1n)(5 + -1n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-3, 5}
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