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Simplifying 5(3 + -3n) + -1(7 + 12n) = n + -4(-4 + n) (3 * 5 + -3n * 5) + -1(7 + 12n) = n + -4(-4 + n) (15 + -15n) + -1(7 + 12n) = n + -4(-4 + n) 15 + -15n + (7 * -1 + 12n * -1) = n + -4(-4 + n) 15 + -15n + (-7 + -12n) = n + -4(-4 + n) Reorder the terms: 15 + -7 + -15n + -12n = n + -4(-4 + n) Combine like terms: 15 + -7 = 8 8 + -15n + -12n = n + -4(-4 + n) Combine like terms: -15n + -12n = -27n 8 + -27n = n + -4(-4 + n) 8 + -27n = n + (-4 * -4 + n * -4) 8 + -27n = n + (16 + -4n) Reorder the terms: 8 + -27n = 16 + n + -4n Combine like terms: n + -4n = -3n 8 + -27n = 16 + -3n Solving 8 + -27n = 16 + -3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3n' to each side of the equation. 8 + -27n + 3n = 16 + -3n + 3n Combine like terms: -27n + 3n = -24n 8 + -24n = 16 + -3n + 3n Combine like terms: -3n + 3n = 0 8 + -24n = 16 + 0 8 + -24n = 16 Add '-8' to each side of the equation. 8 + -8 + -24n = 16 + -8 Combine like terms: 8 + -8 = 0 0 + -24n = 16 + -8 -24n = 16 + -8 Combine like terms: 16 + -8 = 8 -24n = 8 Divide each side by '-24'. n = -0.3333333333 Simplifying n = -0.3333333333
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