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Simplifying 3n + 1(n + -6) = 3n(n + -5) Reorder the terms: 3n + 1(-6 + n) = 3n(n + -5) 3n + (-6 * 1 + n * 1) = 3n(n + -5) 3n + (-6 + 1n) = 3n(n + -5) Reorder the terms: -6 + 3n + 1n = 3n(n + -5) Combine like terms: 3n + 1n = 4n -6 + 4n = 3n(n + -5) Reorder the terms: -6 + 4n = 3n(-5 + n) -6 + 4n = (-5 * 3n + n * 3n) -6 + 4n = (-15n + 3n2) Solving -6 + 4n = -15n + 3n2 Solving for variable 'n'. Combine like terms: 4n + 15n = 19n -6 + 19n + -3n2 = -15n + 3n2 + 15n + -3n2 Reorder the terms: -6 + 19n + -3n2 = -15n + 15n + 3n2 + -3n2 Combine like terms: -15n + 15n = 0 -6 + 19n + -3n2 = 0 + 3n2 + -3n2 -6 + 19n + -3n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 -6 + 19n + -3n2 = 0 Factor a trinomial. (-6 + n)(1 + -3n) = 0Subproblem 1
Set the factor '(-6 + n)' equal to zero and attempt to solve: Simplifying -6 + n = 0 Solving -6 + n = 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 + n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + n = 0 + 6 n = 0 + 6 Combine like terms: 0 + 6 = 6 n = 6 Simplifying n = 6Subproblem 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 = {6, 0.3333333333}
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