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Simplifying 5n + 3(4 + -5n) + 3(3n + 3) + 8(4n + -3) = 0 5n + (4 * 3 + -5n * 3) + 3(3n + 3) + 8(4n + -3) = 0 5n + (12 + -15n) + 3(3n + 3) + 8(4n + -3) = 0 Reorder the terms: 5n + 12 + -15n + 3(3 + 3n) + 8(4n + -3) = 0 5n + 12 + -15n + (3 * 3 + 3n * 3) + 8(4n + -3) = 0 5n + 12 + -15n + (9 + 9n) + 8(4n + -3) = 0 Reorder the terms: 5n + 12 + -15n + 9 + 9n + 8(-3 + 4n) = 0 5n + 12 + -15n + 9 + 9n + (-3 * 8 + 4n * 8) = 0 5n + 12 + -15n + 9 + 9n + (-24 + 32n) = 0 Reorder the terms: 12 + 9 + -24 + 5n + -15n + 9n + 32n = 0 Combine like terms: 12 + 9 = 21 21 + -24 + 5n + -15n + 9n + 32n = 0 Combine like terms: 21 + -24 = -3 -3 + 5n + -15n + 9n + 32n = 0 Combine like terms: 5n + -15n = -10n -3 + -10n + 9n + 32n = 0 Combine like terms: -10n + 9n = -1n -3 + -1n + 32n = 0 Combine like terms: -1n + 32n = 31n -3 + 31n = 0 Solving -3 + 31n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 31n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 31n = 0 + 3 31n = 0 + 3 Combine like terms: 0 + 3 = 3 31n = 3 Divide each side by '31'. n = 0.09677419355 Simplifying n = 0.09677419355
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