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Simplifying 450 = 3n2 + -30n + -150 Reorder the terms: 450 = -150 + -30n + 3n2 Solving 450 = -150 + -30n + 3n2 Solving for variable 'n'. Combine like terms: 450 + 150 = 600 600 + 30n + -3n2 = -150 + -30n + 3n2 + 150 + 30n + -3n2 Reorder the terms: 600 + 30n + -3n2 = -150 + 150 + -30n + 30n + 3n2 + -3n2 Combine like terms: -150 + 150 = 0 600 + 30n + -3n2 = 0 + -30n + 30n + 3n2 + -3n2 600 + 30n + -3n2 = -30n + 30n + 3n2 + -3n2 Combine like terms: -30n + 30n = 0 600 + 30n + -3n2 = 0 + 3n2 + -3n2 600 + 30n + -3n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 600 + 30n + -3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(200 + 10n + -1n2) = 0 Factor a trinomial. 3((20 + -1n)(10 + n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + -1n)' equal to zero and attempt to solve: Simplifying 20 + -1n = 0 Solving 20 + -1n = 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 + -1n = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1n = 0 + -20 -1n = 0 + -20 Combine like terms: 0 + -20 = -20 -1n = -20 Divide each side by '-1'. n = 20 Simplifying n = 20Subproblem 2
Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10Solution
n = {20, -10}
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