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Simplifying (5n + 9)(n + -8) = 0 Reorder the terms: (9 + 5n)(n + -8) = 0 Reorder the terms: (9 + 5n)(-8 + n) = 0 Multiply (9 + 5n) * (-8 + n) (9(-8 + n) + 5n * (-8 + n)) = 0 ((-8 * 9 + n * 9) + 5n * (-8 + n)) = 0 ((-72 + 9n) + 5n * (-8 + n)) = 0 (-72 + 9n + (-8 * 5n + n * 5n)) = 0 (-72 + 9n + (-40n + 5n2)) = 0 Combine like terms: 9n + -40n = -31n (-72 + -31n + 5n2) = 0 Solving -72 + -31n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-9 + -5n)(8 + -1n) = 0Subproblem 1
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 = -1.8Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 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 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-1.8, 8}
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