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Simplifying -42 = -2(1 + 6n) + 8(2 + 5n) -42 = (1 * -2 + 6n * -2) + 8(2 + 5n) -42 = (-2 + -12n) + 8(2 + 5n) -42 = -2 + -12n + (2 * 8 + 5n * 8) -42 = -2 + -12n + (16 + 40n) Reorder the terms: -42 = -2 + 16 + -12n + 40n Combine like terms: -2 + 16 = 14 -42 = 14 + -12n + 40n Combine like terms: -12n + 40n = 28n -42 = 14 + 28n Solving -42 = 14 + 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. -42 + -28n = 14 + 28n + -28n Combine like terms: 28n + -28n = 0 -42 + -28n = 14 + 0 -42 + -28n = 14 Add '42' to each side of the equation. -42 + 42 + -28n = 14 + 42 Combine like terms: -42 + 42 = 0 0 + -28n = 14 + 42 -28n = 14 + 42 Combine like terms: 14 + 42 = 56 -28n = 56 Divide each side by '-28'. n = -2 Simplifying n = -2
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