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Simplifying 3n2 + -21n + 30 = 3 + -3n Reorder the terms: 30 + -21n + 3n2 = 3 + -3n Solving 30 + -21n + 3n2 = 3 + -3n Solving for variable 'n'. Reorder the terms: 30 + -3 + -21n + 3n + 3n2 = 3 + -3n + -3 + 3n Combine like terms: 30 + -3 = 27 27 + -21n + 3n + 3n2 = 3 + -3n + -3 + 3n Combine like terms: -21n + 3n = -18n 27 + -18n + 3n2 = 3 + -3n + -3 + 3n Reorder the terms: 27 + -18n + 3n2 = 3 + -3 + -3n + 3n Combine like terms: 3 + -3 = 0 27 + -18n + 3n2 = 0 + -3n + 3n 27 + -18n + 3n2 = -3n + 3n Combine like terms: -3n + 3n = 0 27 + -18n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -6n + n2) = 0 Factor a trinomial. 3((3 + -1n)(3 + -1n)) = 0 Ignore the factor 3.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 '(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 = 3Solution
n = {3, 3}
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