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Simplifying -54 = 3(4n + -4) + 2(5n + 1) Reorder the terms: -54 = 3(-4 + 4n) + 2(5n + 1) -54 = (-4 * 3 + 4n * 3) + 2(5n + 1) -54 = (-12 + 12n) + 2(5n + 1) Reorder the terms: -54 = -12 + 12n + 2(1 + 5n) -54 = -12 + 12n + (1 * 2 + 5n * 2) -54 = -12 + 12n + (2 + 10n) Reorder the terms: -54 = -12 + 2 + 12n + 10n Combine like terms: -12 + 2 = -10 -54 = -10 + 12n + 10n Combine like terms: 12n + 10n = 22n -54 = -10 + 22n Solving -54 = -10 + 22n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-22n' to each side of the equation. -54 + -22n = -10 + 22n + -22n Combine like terms: 22n + -22n = 0 -54 + -22n = -10 + 0 -54 + -22n = -10 Add '54' to each side of the equation. -54 + 54 + -22n = -10 + 54 Combine like terms: -54 + 54 = 0 0 + -22n = -10 + 54 -22n = -10 + 54 Combine like terms: -10 + 54 = 44 -22n = 44 Divide each side by '-22'. n = -2 Simplifying n = -2
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