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Simplifying (3n + 5)(n + -5) + -3n(n + 7) = 6 Reorder the terms: (5 + 3n)(n + -5) + -3n(n + 7) = 6 Reorder the terms: (5 + 3n)(-5 + n) + -3n(n + 7) = 6 Multiply (5 + 3n) * (-5 + n) (5(-5 + n) + 3n * (-5 + n)) + -3n(n + 7) = 6 ((-5 * 5 + n * 5) + 3n * (-5 + n)) + -3n(n + 7) = 6 ((-25 + 5n) + 3n * (-5 + n)) + -3n(n + 7) = 6 (-25 + 5n + (-5 * 3n + n * 3n)) + -3n(n + 7) = 6 (-25 + 5n + (-15n + 3n2)) + -3n(n + 7) = 6 Combine like terms: 5n + -15n = -10n (-25 + -10n + 3n2) + -3n(n + 7) = 6 Reorder the terms: -25 + -10n + 3n2 + -3n(7 + n) = 6 -25 + -10n + 3n2 + (7 * -3n + n * -3n) = 6 -25 + -10n + 3n2 + (-21n + -3n2) = 6 Reorder the terms: -25 + -10n + -21n + 3n2 + -3n2 = 6 Combine like terms: -10n + -21n = -31n -25 + -31n + 3n2 + -3n2 = 6 Combine like terms: 3n2 + -3n2 = 0 -25 + -31n + 0 = 6 -25 + -31n = 6 Solving -25 + -31n = 6 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 + -31n = 6 + 25 Combine like terms: -25 + 25 = 0 0 + -31n = 6 + 25 -31n = 6 + 25 Combine like terms: 6 + 25 = 31 -31n = 31 Divide each side by '-31'. n = -1 Simplifying n = -1
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