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Simplifying 0 = -3 + -3n2 + 10n Reorder the terms: 0 = -3 + 10n + -3n2 Solving 0 = -3 + 10n + -3n2 Solving for variable 'n'. Combine like terms: 0 + 3 = 3 3 + -10n + 3n2 = -3 + 10n + -3n2 + 3 + -10n + 3n2 Reorder the terms: 3 + -10n + 3n2 = -3 + 3 + 10n + -10n + -3n2 + 3n2 Combine like terms: -3 + 3 = 0 3 + -10n + 3n2 = 0 + 10n + -10n + -3n2 + 3n2 3 + -10n + 3n2 = 10n + -10n + -3n2 + 3n2 Combine like terms: 10n + -10n = 0 3 + -10n + 3n2 = 0 + -3n2 + 3n2 3 + -10n + 3n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 3 + -10n + 3n2 = 0 Factor a trinomial. (1 + -3n)(3 + -1n) = 0Subproblem 1
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 = 0.3333333333Subproblem 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 = {0.3333333333, 3}
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