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Simplifying n(n + 4) + 28 = (n + 1)(n + 8) Reorder the terms: n(4 + n) + 28 = (n + 1)(n + 8) (4 * n + n * n) + 28 = (n + 1)(n + 8) (4n + n2) + 28 = (n + 1)(n + 8) Reorder the terms: 28 + 4n + n2 = (n + 1)(n + 8) Reorder the terms: 28 + 4n + n2 = (1 + n)(n + 8) Reorder the terms: 28 + 4n + n2 = (1 + n)(8 + n) Multiply (1 + n) * (8 + n) 28 + 4n + n2 = (1(8 + n) + n(8 + n)) 28 + 4n + n2 = ((8 * 1 + n * 1) + n(8 + n)) 28 + 4n + n2 = ((8 + 1n) + n(8 + n)) 28 + 4n + n2 = (8 + 1n + (8 * n + n * n)) 28 + 4n + n2 = (8 + 1n + (8n + n2)) Combine like terms: 1n + 8n = 9n 28 + 4n + n2 = (8 + 9n + n2) Add '-1n2' to each side of the equation. 28 + 4n + n2 + -1n2 = 8 + 9n + n2 + -1n2 Combine like terms: n2 + -1n2 = 0 28 + 4n + 0 = 8 + 9n + n2 + -1n2 28 + 4n = 8 + 9n + n2 + -1n2 Combine like terms: n2 + -1n2 = 0 28 + 4n = 8 + 9n + 0 28 + 4n = 8 + 9n Solving 28 + 4n = 8 + 9n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9n' to each side of the equation. 28 + 4n + -9n = 8 + 9n + -9n Combine like terms: 4n + -9n = -5n 28 + -5n = 8 + 9n + -9n Combine like terms: 9n + -9n = 0 28 + -5n = 8 + 0 28 + -5n = 8 Add '-28' to each side of the equation. 28 + -28 + -5n = 8 + -28 Combine like terms: 28 + -28 = 0 0 + -5n = 8 + -28 -5n = 8 + -28 Combine like terms: 8 + -28 = -20 -5n = -20 Divide each side by '-5'. n = 4 Simplifying n = 4
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