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Simplifying 33n2 + -82n + 45 = 0 Reorder the terms: 45 + -82n + 33n2 = 0 Solving 45 + -82n + 33n2 = 0 Solving for variable 'n'. Factor a trinomial. (9 + -11n)(5 + -3n) = 0Subproblem 1
Set the factor '(9 + -11n)' equal to zero and attempt to solve: Simplifying 9 + -11n = 0 Solving 9 + -11n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -11n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -11n = 0 + -9 -11n = 0 + -9 Combine like terms: 0 + -9 = -9 -11n = -9 Divide each side by '-11'. n = 0.8181818182 Simplifying n = 0.8181818182Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {0.8181818182, 1.666666667}
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