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Simplifying 4n2 = -10n + 66 Reorder the terms: 4n2 = 66 + -10n Solving 4n2 = 66 + -10n Solving for variable 'n'. Reorder the terms: -66 + 10n + 4n2 = 66 + -10n + -66 + 10n Reorder the terms: -66 + 10n + 4n2 = 66 + -66 + -10n + 10n Combine like terms: 66 + -66 = 0 -66 + 10n + 4n2 = 0 + -10n + 10n -66 + 10n + 4n2 = -10n + 10n Combine like terms: -10n + 10n = 0 -66 + 10n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 5n + 2n2) = 0 Factor a trinomial. 2((-11 + -2n)(3 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -2n)' equal to zero and attempt to solve: Simplifying -11 + -2n = 0 Solving -11 + -2n = 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 + -2n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2n = 0 + 11 -2n = 0 + 11 Combine like terms: 0 + 11 = 11 -2n = 11 Divide each side by '-2'. n = -5.5 Simplifying n = -5.5Subproblem 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 = {-5.5, 3}
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