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Simplifying 3n2 + 10n + -37 = 8 + 4n Reorder the terms: -37 + 10n + 3n2 = 8 + 4n Solving -37 + 10n + 3n2 = 8 + 4n Solving for variable 'n'. Reorder the terms: -37 + -8 + 10n + -4n + 3n2 = 8 + 4n + -8 + -4n Combine like terms: -37 + -8 = -45 -45 + 10n + -4n + 3n2 = 8 + 4n + -8 + -4n Combine like terms: 10n + -4n = 6n -45 + 6n + 3n2 = 8 + 4n + -8 + -4n Reorder the terms: -45 + 6n + 3n2 = 8 + -8 + 4n + -4n Combine like terms: 8 + -8 = 0 -45 + 6n + 3n2 = 0 + 4n + -4n -45 + 6n + 3n2 = 4n + -4n Combine like terms: 4n + -4n = 0 -45 + 6n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 2n + n2) = 0 Factor a trinomial. 3((-5 + -1n)(3 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 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 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5Subproblem 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 = {-5, 3}
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