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Simplifying 0 = 56 + 27n + -5n2 Solving 0 = 56 + 27n + -5n2 Solving for variable 'n'. Combine like terms: 0 + -56 = -56 -56 + -27n + 5n2 = 56 + 27n + -5n2 + -56 + -27n + 5n2 Reorder the terms: -56 + -27n + 5n2 = 56 + -56 + 27n + -27n + -5n2 + 5n2 Combine like terms: 56 + -56 = 0 -56 + -27n + 5n2 = 0 + 27n + -27n + -5n2 + 5n2 -56 + -27n + 5n2 = 27n + -27n + -5n2 + 5n2 Combine like terms: 27n + -27n = 0 -56 + -27n + 5n2 = 0 + -5n2 + 5n2 -56 + -27n + 5n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 -56 + -27n + 5n2 = 0 Factor a trinomial. (-8 + -5n)(7 + -1n) = 0Subproblem 1
Set the factor '(-8 + -5n)' equal to zero and attempt to solve: Simplifying -8 + -5n = 0 Solving -8 + -5n = 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 + -5n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5n = 0 + 8 -5n = 0 + 8 Combine like terms: 0 + 8 = 8 -5n = 8 Divide each side by '-5'. n = -1.6 Simplifying n = -1.6Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-1.6, 7}
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