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Simplifying (N) + (n + 1)(n + 2) = -84 N + (n + 1)(n + 2) = -84 Reorder the terms: N + (1 + n)(n + 2) = -84 Reorder the terms: N + (1 + n)(2 + n) = -84 Multiply (1 + n) * (2 + n) N + (1(2 + n) + n(2 + n)) = -84 N + ((2 * 1 + n * 1) + n(2 + n)) = -84 N + ((2 + 1n) + n(2 + n)) = -84 N + (2 + 1n + (2 * n + n * n)) = -84 N + (2 + 1n + (2n + n2)) = -84 Combine like terms: 1n + 2n = 3n N + (2 + 3n + n2) = -84 Reorder the terms: 2 + N + 3n + n2 = -84 Solving 2 + N + 3n + n2 = -84 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + N + 3n + -2 + n2 = -84 + -2 Reorder the terms: 2 + -2 + N + 3n + n2 = -84 + -2 Combine like terms: 2 + -2 = 0 0 + N + 3n + n2 = -84 + -2 N + 3n + n2 = -84 + -2 Combine like terms: -84 + -2 = -86 N + 3n + n2 = -86 Add '-3n' to each side of the equation. N + 3n + -3n + n2 = -86 + -3n Combine like terms: 3n + -3n = 0 N + 0 + n2 = -86 + -3n N + n2 = -86 + -3n Add '-1n2' to each side of the equation. N + n2 + -1n2 = -86 + -3n + -1n2 Combine like terms: n2 + -1n2 = 0 N + 0 = -86 + -3n + -1n2 N = -86 + -3n + -1n2 Simplifying N = -86 + -3n + -1n2
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