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Simplifying [9(n + 5) + -19] + -1[3(n + -4) + 2] = 0 Reorder the terms: [9(5 + n) + -19] + -1[3(n + -4) + 2] = 0 [(5 * 9 + n * 9) + -19] + -1[3(n + -4) + 2] = 0 [(45 + 9n) + -19] + -1[3(n + -4) + 2] = 0 Reorder the terms: [45 + -19 + 9n] + -1[3(n + -4) + 2] = 0 Combine like terms: 45 + -19 = 26 [26 + 9n] + -1[3(n + -4) + 2] = 0 Remove brackets around [26 + 9n] 26 + 9n + -1[3(n + -4) + 2] = 0 Reorder the terms: 26 + 9n + -1[3(-4 + n) + 2] = 0 26 + 9n + -1[(-4 * 3 + n * 3) + 2] = 0 26 + 9n + -1[(-12 + 3n) + 2] = 0 Reorder the terms: 26 + 9n + -1[-12 + 2 + 3n] = 0 Combine like terms: -12 + 2 = -10 26 + 9n + -1[-10 + 3n] = 0 26 + 9n + [-10 * -1 + 3n * -1] = 0 26 + 9n + [10 + -3n] = 0 Reorder the terms: 26 + 10 + 9n + -3n = 0 Combine like terms: 26 + 10 = 36 36 + 9n + -3n = 0 Combine like terms: 9n + -3n = 6n 36 + 6n = 0 Solving 36 + 6n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + 6n = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 6n = 0 + -36 6n = 0 + -36 Combine like terms: 0 + -36 = -36 6n = -36 Divide each side by '6'. n = -6 Simplifying n = -6
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