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Simplifying 5(2n + -3) + 3(4n + 2) + -1(n + 5) = 0 Reorder the terms: 5(-3 + 2n) + 3(4n + 2) + -1(n + 5) = 0 (-3 * 5 + 2n * 5) + 3(4n + 2) + -1(n + 5) = 0 (-15 + 10n) + 3(4n + 2) + -1(n + 5) = 0 Reorder the terms: -15 + 10n + 3(2 + 4n) + -1(n + 5) = 0 -15 + 10n + (2 * 3 + 4n * 3) + -1(n + 5) = 0 -15 + 10n + (6 + 12n) + -1(n + 5) = 0 Reorder the terms: -15 + 10n + 6 + 12n + -1(5 + n) = 0 -15 + 10n + 6 + 12n + (5 * -1 + n * -1) = 0 -15 + 10n + 6 + 12n + (-5 + -1n) = 0 Reorder the terms: -15 + 6 + -5 + 10n + 12n + -1n = 0 Combine like terms: -15 + 6 = -9 -9 + -5 + 10n + 12n + -1n = 0 Combine like terms: -9 + -5 = -14 -14 + 10n + 12n + -1n = 0 Combine like terms: 10n + 12n = 22n -14 + 22n + -1n = 0 Combine like terms: 22n + -1n = 21n -14 + 21n = 0 Solving -14 + 21n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 21n = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 21n = 0 + 14 21n = 0 + 14 Combine like terms: 0 + 14 = 14 21n = 14 Divide each side by '21'. n = 0.6666666667 Simplifying n = 0.6666666667
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