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Simplifying (n + -84)(n + -9) = 0 Reorder the terms: (-84 + n)(n + -9) = 0 Reorder the terms: (-84 + n)(-9 + n) = 0 Multiply (-84 + n) * (-9 + n) (-84(-9 + n) + n(-9 + n)) = 0 ((-9 * -84 + n * -84) + n(-9 + n)) = 0 ((756 + -84n) + n(-9 + n)) = 0 (756 + -84n + (-9 * n + n * n)) = 0 (756 + -84n + (-9n + n2)) = 0 Combine like terms: -84n + -9n = -93n (756 + -93n + n2) = 0 Solving 756 + -93n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (9 + -1n)(84 + -1n) = 0Subproblem 1
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Subproblem 2
Set the factor '(84 + -1n)' equal to zero and attempt to solve: Simplifying 84 + -1n = 0 Solving 84 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-84' to each side of the equation. 84 + -84 + -1n = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -1n = 0 + -84 -1n = 0 + -84 Combine like terms: 0 + -84 = -84 -1n = -84 Divide each side by '-1'. n = 84 Simplifying n = 84Solution
n = {9, 84}
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