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Simplifying 0 = 3n2 + -66n + 363 Reorder the terms: 0 = 363 + -66n + 3n2 Solving 0 = 363 + -66n + 3n2 Solving for variable 'n'. Combine like terms: 0 + -363 = -363 -363 + 66n + -3n2 = 363 + -66n + 3n2 + -363 + 66n + -3n2 Reorder the terms: -363 + 66n + -3n2 = 363 + -363 + -66n + 66n + 3n2 + -3n2 Combine like terms: 363 + -363 = 0 -363 + 66n + -3n2 = 0 + -66n + 66n + 3n2 + -3n2 -363 + 66n + -3n2 = -66n + 66n + 3n2 + -3n2 Combine like terms: -66n + 66n = 0 -363 + 66n + -3n2 = 0 + 3n2 + -3n2 -363 + 66n + -3n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 -363 + 66n + -3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-121 + 22n + -1n2) = 0 Factor a trinomial. 3((-11 + n)(11 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + n)' equal to zero and attempt to solve: Simplifying -11 + n = 0 Solving -11 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + n = 0 + 11 n = 0 + 11 Combine like terms: 0 + 11 = 11 n = 11 Simplifying n = 11Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve: Simplifying 11 + -1n = 0 Solving 11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1n = 0 + -11 -1n = 0 + -11 Combine like terms: 0 + -11 = -11 -1n = -11 Divide each side by '-1'. n = 11 Simplifying n = 11Solution
n = {11, 11}
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