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Simplifying 3(4n + -1) + -1(3n + 2) = 4(n + -5) Reorder the terms: 3(-1 + 4n) + -1(3n + 2) = 4(n + -5) (-1 * 3 + 4n * 3) + -1(3n + 2) = 4(n + -5) (-3 + 12n) + -1(3n + 2) = 4(n + -5) Reorder the terms: -3 + 12n + -1(2 + 3n) = 4(n + -5) -3 + 12n + (2 * -1 + 3n * -1) = 4(n + -5) -3 + 12n + (-2 + -3n) = 4(n + -5) Reorder the terms: -3 + -2 + 12n + -3n = 4(n + -5) Combine like terms: -3 + -2 = -5 -5 + 12n + -3n = 4(n + -5) Combine like terms: 12n + -3n = 9n -5 + 9n = 4(n + -5) Reorder the terms: -5 + 9n = 4(-5 + n) -5 + 9n = (-5 * 4 + n * 4) -5 + 9n = (-20 + 4n) Solving -5 + 9n = -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. -5 + 9n + -4n = -20 + 4n + -4n Combine like terms: 9n + -4n = 5n -5 + 5n = -20 + 4n + -4n Combine like terms: 4n + -4n = 0 -5 + 5n = -20 + 0 -5 + 5n = -20 Add '5' to each side of the equation. -5 + 5 + 5n = -20 + 5 Combine like terms: -5 + 5 = 0 0 + 5n = -20 + 5 5n = -20 + 5 Combine like terms: -20 + 5 = -15 5n = -15 Divide each side by '5'. n = -3 Simplifying n = -3
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