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Simplifying 9(n + -8) + -5n(n + -8) = 0 Reorder the terms: 9(-8 + n) + -5n(n + -8) = 0 (-8 * 9 + n * 9) + -5n(n + -8) = 0 (-72 + 9n) + -5n(n + -8) = 0 Reorder the terms: -72 + 9n + -5n(-8 + n) = 0 -72 + 9n + (-8 * -5n + n * -5n) = 0 -72 + 9n + (40n + -5n2) = 0 Combine like terms: 9n + 40n = 49n -72 + 49n + -5n2 = 0 Solving -72 + 49n + -5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + n)(9 + -5n) = 0Subproblem 1
Set the factor '(-8 + n)' equal to zero and attempt to solve: Simplifying -8 + n = 0 Solving -8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + n = 0 + 8 n = 0 + 8 Combine like terms: 0 + 8 = 8 n = 8 Simplifying n = 8Subproblem 2
Set the factor '(9 + -5n)' equal to zero and attempt to solve: Simplifying 9 + -5n = 0 Solving 9 + -5n = 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 + -5n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5n = 0 + -9 -5n = 0 + -9 Combine like terms: 0 + -9 = -9 -5n = -9 Divide each side by '-5'. n = 1.8 Simplifying n = 1.8Solution
n = {8, 1.8}
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