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Simplifying 3n2 + 75 = 30n Reorder the terms: 75 + 3n2 = 30n Solving 75 + 3n2 = 30n Solving for variable 'n'. Reorder the terms: 75 + -30n + 3n2 = 30n + -30n Combine like terms: 30n + -30n = 0 75 + -30n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -10n + n2) = 0 Factor a trinomial. 3((5 + -1n)(5 + -1n)) = 0 Ignore the factor 3.Subproblem 1
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 = 5Subproblem 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 = {5, 5}
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