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Simplifying (n + 5)(n + -2) = 144 Reorder the terms: (5 + n)(n + -2) = 144 Reorder the terms: (5 + n)(-2 + n) = 144 Multiply (5 + n) * (-2 + n) (5(-2 + n) + n(-2 + n)) = 144 ((-2 * 5 + n * 5) + n(-2 + n)) = 144 ((-10 + 5n) + n(-2 + n)) = 144 (-10 + 5n + (-2 * n + n * n)) = 144 (-10 + 5n + (-2n + n2)) = 144 Combine like terms: 5n + -2n = 3n (-10 + 3n + n2) = 144 Solving -10 + 3n + n2 = 144 Solving for variable 'n'. Reorder the terms: -10 + -144 + 3n + n2 = 144 + -144 Combine like terms: -10 + -144 = -154 -154 + 3n + n2 = 144 + -144 Combine like terms: 144 + -144 = 0 -154 + 3n + n2 = 0 Factor a trinomial. (-14 + -1n)(11 + -1n) = 0Subproblem 1
Set the factor '(-14 + -1n)' equal to zero and attempt to solve: Simplifying -14 + -1n = 0 Solving -14 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1n = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1n = 0 + 14 -1n = 0 + 14 Combine like terms: 0 + 14 = 14 -1n = 14 Divide each side by '-1'. n = -14 Simplifying n = -14Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve: Simplifying 11 + -1n = 0 Solving 11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1n = 0 + -11 -1n = 0 + -11 Combine like terms: 0 + -11 = -11 -1n = -11 Divide each side by '-1'. n = 11 Simplifying n = 11Solution
n = {-14, 11}
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