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Simplifying 57n2 + 78n + -30 = 6n + 3n2 Reorder the terms: -30 + 78n + 57n2 = 6n + 3n2 Solving -30 + 78n + 57n2 = 6n + 3n2 Solving for variable 'n'. Reorder the terms: -30 + 78n + -6n + 57n2 + -3n2 = 6n + 3n2 + -6n + -3n2 Combine like terms: 78n + -6n = 72n -30 + 72n + 57n2 + -3n2 = 6n + 3n2 + -6n + -3n2 Combine like terms: 57n2 + -3n2 = 54n2 -30 + 72n + 54n2 = 6n + 3n2 + -6n + -3n2 Reorder the terms: -30 + 72n + 54n2 = 6n + -6n + 3n2 + -3n2 Combine like terms: 6n + -6n = 0 -30 + 72n + 54n2 = 0 + 3n2 + -3n2 -30 + 72n + 54n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 -30 + 72n + 54n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + 12n + 9n2) = 0 Factor a trinomial. 6((-5 + -3n)(1 + -3n)) = 0 Ignore the factor 6.Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-1.666666667, 0.3333333333}
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