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Simplifying [7(n + 5) + -16] + -1[3(n + -4) + 3] = 0 Reorder the terms: [7(5 + n) + -16] + -1[3(n + -4) + 3] = 0 [(5 * 7 + n * 7) + -16] + -1[3(n + -4) + 3] = 0 [(35 + 7n) + -16] + -1[3(n + -4) + 3] = 0 Reorder the terms: [35 + -16 + 7n] + -1[3(n + -4) + 3] = 0 Combine like terms: 35 + -16 = 19 [19 + 7n] + -1[3(n + -4) + 3] = 0 Remove brackets around [19 + 7n] 19 + 7n + -1[3(n + -4) + 3] = 0 Reorder the terms: 19 + 7n + -1[3(-4 + n) + 3] = 0 19 + 7n + -1[(-4 * 3 + n * 3) + 3] = 0 19 + 7n + -1[(-12 + 3n) + 3] = 0 Reorder the terms: 19 + 7n + -1[-12 + 3 + 3n] = 0 Combine like terms: -12 + 3 = -9 19 + 7n + -1[-9 + 3n] = 0 19 + 7n + [-9 * -1 + 3n * -1] = 0 19 + 7n + [9 + -3n] = 0 Reorder the terms: 19 + 9 + 7n + -3n = 0 Combine like terms: 19 + 9 = 28 28 + 7n + -3n = 0 Combine like terms: 7n + -3n = 4n 28 + 4n = 0 Solving 28 + 4n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + 4n = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 4n = 0 + -28 4n = 0 + -28 Combine like terms: 0 + -28 = -28 4n = -28 Divide each side by '4'. n = -7 Simplifying n = -7
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