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Simplifying -2 + 6(3n + -5) = 7(4n + 7) + 3 Reorder the terms: -2 + 6(-5 + 3n) = 7(4n + 7) + 3 -2 + (-5 * 6 + 3n * 6) = 7(4n + 7) + 3 -2 + (-30 + 18n) = 7(4n + 7) + 3 Combine like terms: -2 + -30 = -32 -32 + 18n = 7(4n + 7) + 3 Reorder the terms: -32 + 18n = 7(7 + 4n) + 3 -32 + 18n = (7 * 7 + 4n * 7) + 3 -32 + 18n = (49 + 28n) + 3 Reorder the terms: -32 + 18n = 49 + 3 + 28n Combine like terms: 49 + 3 = 52 -32 + 18n = 52 + 28n Solving -32 + 18n = 52 + 28n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-28n' to each side of the equation. -32 + 18n + -28n = 52 + 28n + -28n Combine like terms: 18n + -28n = -10n -32 + -10n = 52 + 28n + -28n Combine like terms: 28n + -28n = 0 -32 + -10n = 52 + 0 -32 + -10n = 52 Add '32' to each side of the equation. -32 + 32 + -10n = 52 + 32 Combine like terms: -32 + 32 = 0 0 + -10n = 52 + 32 -10n = 52 + 32 Combine like terms: 52 + 32 = 84 -10n = 84 Divide each side by '-10'. n = -8.4 Simplifying n = -8.4
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