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Simplifying (4 + -1n)(5 + -1n) = 0 Multiply (4 + -1n) * (5 + -1n) (4(5 + -1n) + -1n * (5 + -1n)) = 0 ((5 * 4 + -1n * 4) + -1n * (5 + -1n)) = 0 ((20 + -4n) + -1n * (5 + -1n)) = 0 (20 + -4n + (5 * -1n + -1n * -1n)) = 0 (20 + -4n + (-5n + 1n2)) = 0 Combine like terms: -4n + -5n = -9n (20 + -9n + 1n2) = 0 Solving 20 + -9n + 1n2 = 0 Solving for variable 'n'. Factor a trinomial. (4 + -1n)(5 + -1n) = 0Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {4, 5}
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