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Simplifying 12(3n + 2p) + 11(n + 3(2n + -1p + -3)) = 0 (3n * 12 + 2p * 12) + 11(n + 3(2n + -1p + -3)) = 0 (36n + 24p) + 11(n + 3(2n + -1p + -3)) = 0 Reorder the terms: 36n + 24p + 11(n + 3(-3 + 2n + -1p)) = 0 36n + 24p + 11(n + (-3 * 3 + 2n * 3 + -1p * 3)) = 0 36n + 24p + 11(n + (-9 + 6n + -3p)) = 0 Reorder the terms: 36n + 24p + 11(-9 + n + 6n + -3p) = 0 Combine like terms: n + 6n = 7n 36n + 24p + 11(-9 + 7n + -3p) = 0 36n + 24p + (-9 * 11 + 7n * 11 + -3p * 11) = 0 36n + 24p + (-99 + 77n + -33p) = 0 Reorder the terms: -99 + 36n + 77n + 24p + -33p = 0 Combine like terms: 36n + 77n = 113n -99 + 113n + 24p + -33p = 0 Combine like terms: 24p + -33p = -9p -99 + 113n + -9p = 0 Solving -99 + 113n + -9p = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '99' to each side of the equation. -99 + 113n + 99 + -9p = 0 + 99 Reorder the terms: -99 + 99 + 113n + -9p = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 113n + -9p = 0 + 99 113n + -9p = 0 + 99 Combine like terms: 0 + 99 = 99 113n + -9p = 99 Add '9p' to each side of the equation. 113n + -9p + 9p = 99 + 9p Combine like terms: -9p + 9p = 0 113n + 0 = 99 + 9p 113n = 99 + 9p Divide each side by '113'. n = 0.8761061947 + 0.0796460177p Simplifying n = 0.8761061947 + 0.0796460177p
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