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Simplifying (8n + -1)(3n + -5) = (4n + 3)(6n + 5) Reorder the terms: (-1 + 8n)(3n + -5) = (4n + 3)(6n + 5) Reorder the terms: (-1 + 8n)(-5 + 3n) = (4n + 3)(6n + 5) Multiply (-1 + 8n) * (-5 + 3n) (-1(-5 + 3n) + 8n * (-5 + 3n)) = (4n + 3)(6n + 5) ((-5 * -1 + 3n * -1) + 8n * (-5 + 3n)) = (4n + 3)(6n + 5) ((5 + -3n) + 8n * (-5 + 3n)) = (4n + 3)(6n + 5) (5 + -3n + (-5 * 8n + 3n * 8n)) = (4n + 3)(6n + 5) (5 + -3n + (-40n + 24n2)) = (4n + 3)(6n + 5) Combine like terms: -3n + -40n = -43n (5 + -43n + 24n2) = (4n + 3)(6n + 5) Reorder the terms: 5 + -43n + 24n2 = (3 + 4n)(6n + 5) Reorder the terms: 5 + -43n + 24n2 = (3 + 4n)(5 + 6n) Multiply (3 + 4n) * (5 + 6n) 5 + -43n + 24n2 = (3(5 + 6n) + 4n * (5 + 6n)) 5 + -43n + 24n2 = ((5 * 3 + 6n * 3) + 4n * (5 + 6n)) 5 + -43n + 24n2 = ((15 + 18n) + 4n * (5 + 6n)) 5 + -43n + 24n2 = (15 + 18n + (5 * 4n + 6n * 4n)) 5 + -43n + 24n2 = (15 + 18n + (20n + 24n2)) Combine like terms: 18n + 20n = 38n 5 + -43n + 24n2 = (15 + 38n + 24n2) Add '-24n2' to each side of the equation. 5 + -43n + 24n2 + -24n2 = 15 + 38n + 24n2 + -24n2 Combine like terms: 24n2 + -24n2 = 0 5 + -43n + 0 = 15 + 38n + 24n2 + -24n2 5 + -43n = 15 + 38n + 24n2 + -24n2 Combine like terms: 24n2 + -24n2 = 0 5 + -43n = 15 + 38n + 0 5 + -43n = 15 + 38n Solving 5 + -43n = 15 + 38n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-38n' to each side of the equation. 5 + -43n + -38n = 15 + 38n + -38n Combine like terms: -43n + -38n = -81n 5 + -81n = 15 + 38n + -38n Combine like terms: 38n + -38n = 0 5 + -81n = 15 + 0 5 + -81n = 15 Add '-5' to each side of the equation. 5 + -5 + -81n = 15 + -5 Combine like terms: 5 + -5 = 0 0 + -81n = 15 + -5 -81n = 15 + -5 Combine like terms: 15 + -5 = 10 -81n = 10 Divide each side by '-81'. n = -0.1234567901 Simplifying n = -0.1234567901
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