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Simplifying -12(10n + 7) + 9(5n + -6) = 8 + 4n + 12 Reorder the terms: -12(7 + 10n) + 9(5n + -6) = 8 + 4n + 12 (7 * -12 + 10n * -12) + 9(5n + -6) = 8 + 4n + 12 (-84 + -120n) + 9(5n + -6) = 8 + 4n + 12 Reorder the terms: -84 + -120n + 9(-6 + 5n) = 8 + 4n + 12 -84 + -120n + (-6 * 9 + 5n * 9) = 8 + 4n + 12 -84 + -120n + (-54 + 45n) = 8 + 4n + 12 Reorder the terms: -84 + -54 + -120n + 45n = 8 + 4n + 12 Combine like terms: -84 + -54 = -138 -138 + -120n + 45n = 8 + 4n + 12 Combine like terms: -120n + 45n = -75n -138 + -75n = 8 + 4n + 12 Reorder the terms: -138 + -75n = 8 + 12 + 4n Combine like terms: 8 + 12 = 20 -138 + -75n = 20 + 4n Solving -138 + -75n = 20 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. -138 + -75n + -4n = 20 + 4n + -4n Combine like terms: -75n + -4n = -79n -138 + -79n = 20 + 4n + -4n Combine like terms: 4n + -4n = 0 -138 + -79n = 20 + 0 -138 + -79n = 20 Add '138' to each side of the equation. -138 + 138 + -79n = 20 + 138 Combine like terms: -138 + 138 = 0 0 + -79n = 20 + 138 -79n = 20 + 138 Combine like terms: 20 + 138 = 158 -79n = 158 Divide each side by '-79'. n = -2 Simplifying n = -2
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