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Simplifying 3n + -4 + 1 + -6n = 3(3 + 5n) + -6(5n + -6) Reorder the terms: -4 + 1 + 3n + -6n = 3(3 + 5n) + -6(5n + -6) Combine like terms: -4 + 1 = -3 -3 + 3n + -6n = 3(3 + 5n) + -6(5n + -6) Combine like terms: 3n + -6n = -3n -3 + -3n = 3(3 + 5n) + -6(5n + -6) -3 + -3n = (3 * 3 + 5n * 3) + -6(5n + -6) -3 + -3n = (9 + 15n) + -6(5n + -6) Reorder the terms: -3 + -3n = 9 + 15n + -6(-6 + 5n) -3 + -3n = 9 + 15n + (-6 * -6 + 5n * -6) -3 + -3n = 9 + 15n + (36 + -30n) Reorder the terms: -3 + -3n = 9 + 36 + 15n + -30n Combine like terms: 9 + 36 = 45 -3 + -3n = 45 + 15n + -30n Combine like terms: 15n + -30n = -15n -3 + -3n = 45 + -15n Solving -3 + -3n = 45 + -15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '15n' to each side of the equation. -3 + -3n + 15n = 45 + -15n + 15n Combine like terms: -3n + 15n = 12n -3 + 12n = 45 + -15n + 15n Combine like terms: -15n + 15n = 0 -3 + 12n = 45 + 0 -3 + 12n = 45 Add '3' to each side of the equation. -3 + 3 + 12n = 45 + 3 Combine like terms: -3 + 3 = 0 0 + 12n = 45 + 3 12n = 45 + 3 Combine like terms: 45 + 3 = 48 12n = 48 Divide each side by '12'. n = 4 Simplifying n = 4
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