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Simplifying (n + 2)(n + 1) = 600 Reorder the terms: (2 + n)(n + 1) = 600 Reorder the terms: (2 + n)(1 + n) = 600 Multiply (2 + n) * (1 + n) (2(1 + n) + n(1 + n)) = 600 ((1 * 2 + n * 2) + n(1 + n)) = 600 ((2 + 2n) + n(1 + n)) = 600 (2 + 2n + (1 * n + n * n)) = 600 (2 + 2n + (1n + n2)) = 600 Combine like terms: 2n + 1n = 3n (2 + 3n + n2) = 600 Solving 2 + 3n + n2 = 600 Solving for variable 'n'. Reorder the terms: 2 + -600 + 3n + n2 = 600 + -600 Combine like terms: 2 + -600 = -598 -598 + 3n + n2 = 600 + -600 Combine like terms: 600 + -600 = 0 -598 + 3n + n2 = 0 Factor a trinomial. (-26 + -1n)(23 + -1n) = 0Subproblem 1
Set the factor '(-26 + -1n)' equal to zero and attempt to solve: Simplifying -26 + -1n = 0 Solving -26 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + -1n = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -1n = 0 + 26 -1n = 0 + 26 Combine like terms: 0 + 26 = 26 -1n = 26 Divide each side by '-1'. n = -26 Simplifying n = -26Subproblem 2
Set the factor '(23 + -1n)' equal to zero and attempt to solve: Simplifying 23 + -1n = 0 Solving 23 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -1n = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -1n = 0 + -23 -1n = 0 + -23 Combine like terms: 0 + -23 = -23 -1n = -23 Divide each side by '-1'. n = 23 Simplifying n = 23Solution
n = {-26, 23}
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