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Simplifying n2 + -5n + -36 = -4 + -1n Reorder the terms: -36 + -5n + n2 = -4 + -1n Solving -36 + -5n + n2 = -4 + -1n Solving for variable 'n'. Reorder the terms: -36 + 4 + -5n + n + n2 = -4 + -1n + 4 + n Combine like terms: -36 + 4 = -32 -32 + -5n + n + n2 = -4 + -1n + 4 + n Combine like terms: -5n + n = -4n -32 + -4n + n2 = -4 + -1n + 4 + n Reorder the terms: -32 + -4n + n2 = -4 + 4 + -1n + n Combine like terms: -4 + 4 = 0 -32 + -4n + n2 = 0 + -1n + n -32 + -4n + n2 = -1n + n Combine like terms: -1n + n = 0 -32 + -4n + n2 = 0 Factor a trinomial. (-4 + -1n)(8 + -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 '(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 = {-4, 8}
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