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Simplifying 9n2 + 33n = 126 Reorder the terms: 33n + 9n2 = 126 Solving 33n + 9n2 = 126 Solving for variable 'n'. Reorder the terms: -126 + 33n + 9n2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 33n + 9n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-42 + 11n + 3n2) = 0 Factor a trinomial. 3((-6 + -1n)(7 + -3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
Set the factor '(7 + -3n)' equal to zero and attempt to solve: Simplifying 7 + -3n = 0 Solving 7 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3n = 0 + -7 -3n = 0 + -7 Combine like terms: 0 + -7 = -7 -3n = -7 Divide each side by '-3'. n = 2.333333333 Simplifying n = 2.333333333Solution
n = {-6, 2.333333333}
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