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Simplifying 12(3n + 2p) + 11(n + 3(2n + -1p + -33)) = 0 (3n * 12 + 2p * 12) + 11(n + 3(2n + -1p + -33)) = 0 (36n + 24p) + 11(n + 3(2n + -1p + -33)) = 0 Reorder the terms: 36n + 24p + 11(n + 3(-33 + 2n + -1p)) = 0 36n + 24p + 11(n + (-33 * 3 + 2n * 3 + -1p * 3)) = 0 36n + 24p + 11(n + (-99 + 6n + -3p)) = 0 Reorder the terms: 36n + 24p + 11(-99 + n + 6n + -3p) = 0 Combine like terms: n + 6n = 7n 36n + 24p + 11(-99 + 7n + -3p) = 0 36n + 24p + (-99 * 11 + 7n * 11 + -3p * 11) = 0 36n + 24p + (-1089 + 77n + -33p) = 0 Reorder the terms: -1089 + 36n + 77n + 24p + -33p = 0 Combine like terms: 36n + 77n = 113n -1089 + 113n + 24p + -33p = 0 Combine like terms: 24p + -33p = -9p -1089 + 113n + -9p = 0 Solving -1089 + 113n + -9p = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1089' to each side of the equation. -1089 + 113n + 1089 + -9p = 0 + 1089 Reorder the terms: -1089 + 1089 + 113n + -9p = 0 + 1089 Combine like terms: -1089 + 1089 = 0 0 + 113n + -9p = 0 + 1089 113n + -9p = 0 + 1089 Combine like terms: 0 + 1089 = 1089 113n + -9p = 1089 Add '9p' to each side of the equation. 113n + -9p + 9p = 1089 + 9p Combine like terms: -9p + 9p = 0 113n + 0 = 1089 + 9p 113n = 1089 + 9p Divide each side by '113'. n = 9.637168142 + 0.0796460177p Simplifying n = 9.637168142 + 0.0796460177p
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