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Simplifying 3(3n + -1) + -4(2n + 3) + 5(-4n + -1) = 0 Reorder the terms: 3(-1 + 3n) + -4(2n + 3) + 5(-4n + -1) = 0 (-1 * 3 + 3n * 3) + -4(2n + 3) + 5(-4n + -1) = 0 (-3 + 9n) + -4(2n + 3) + 5(-4n + -1) = 0 Reorder the terms: -3 + 9n + -4(3 + 2n) + 5(-4n + -1) = 0 -3 + 9n + (3 * -4 + 2n * -4) + 5(-4n + -1) = 0 -3 + 9n + (-12 + -8n) + 5(-4n + -1) = 0 Reorder the terms: -3 + 9n + -12 + -8n + 5(-1 + -4n) = 0 -3 + 9n + -12 + -8n + (-1 * 5 + -4n * 5) = 0 -3 + 9n + -12 + -8n + (-5 + -20n) = 0 Reorder the terms: -3 + -12 + -5 + 9n + -8n + -20n = 0 Combine like terms: -3 + -12 = -15 -15 + -5 + 9n + -8n + -20n = 0 Combine like terms: -15 + -5 = -20 -20 + 9n + -8n + -20n = 0 Combine like terms: 9n + -8n = 1n -20 + 1n + -20n = 0 Combine like terms: 1n + -20n = -19n -20 + -19n = 0 Solving -20 + -19n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -19n = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -19n = 0 + 20 -19n = 0 + 20 Combine like terms: 0 + 20 = 20 -19n = 20 Divide each side by '-19'. n = -1.052631579 Simplifying n = -1.052631579
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