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Simplifying 15n + -1(3n + -5)(4n + 5) = 5 + -12n2 Reorder the terms: 15n + -1(-5 + 3n)(4n + 5) = 5 + -12n2 Reorder the terms: 15n + -1(-5 + 3n)(5 + 4n) = 5 + -12n2 Multiply (-5 + 3n) * (5 + 4n) 15n + -1(-5(5 + 4n) + 3n * (5 + 4n)) = 5 + -12n2 15n + -1((5 * -5 + 4n * -5) + 3n * (5 + 4n)) = 5 + -12n2 15n + -1((-25 + -20n) + 3n * (5 + 4n)) = 5 + -12n2 15n + -1(-25 + -20n + (5 * 3n + 4n * 3n)) = 5 + -12n2 15n + -1(-25 + -20n + (15n + 12n2)) = 5 + -12n2 Combine like terms: -20n + 15n = -5n 15n + -1(-25 + -5n + 12n2) = 5 + -12n2 15n + (-25 * -1 + -5n * -1 + 12n2 * -1) = 5 + -12n2 15n + (25 + 5n + -12n2) = 5 + -12n2 Reorder the terms: 25 + 15n + 5n + -12n2 = 5 + -12n2 Combine like terms: 15n + 5n = 20n 25 + 20n + -12n2 = 5 + -12n2 Add '12n2' to each side of the equation. 25 + 20n + -12n2 + 12n2 = 5 + -12n2 + 12n2 Combine like terms: -12n2 + 12n2 = 0 25 + 20n + 0 = 5 + -12n2 + 12n2 25 + 20n = 5 + -12n2 + 12n2 Combine like terms: -12n2 + 12n2 = 0 25 + 20n = 5 + 0 25 + 20n = 5 Solving 25 + 20n = 5 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 20n = 5 + -25 Combine like terms: 25 + -25 = 0 0 + 20n = 5 + -25 20n = 5 + -25 Combine like terms: 5 + -25 = -20 20n = -20 Divide each side by '20'. n = -1 Simplifying n = -1
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