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Simplifying -1n2 = 6 + -5n + -2n2 Solving -1n2 = 6 + -5n + -2n2 Solving for variable 'n'. Reorder the terms: -6 + 5n + -1n2 + 2n2 = 6 + -5n + -2n2 + -6 + 5n + 2n2 Combine like terms: -1n2 + 2n2 = 1n2 -6 + 5n + 1n2 = 6 + -5n + -2n2 + -6 + 5n + 2n2 Reorder the terms: -6 + 5n + 1n2 = 6 + -6 + -5n + 5n + -2n2 + 2n2 Combine like terms: 6 + -6 = 0 -6 + 5n + 1n2 = 0 + -5n + 5n + -2n2 + 2n2 -6 + 5n + 1n2 = -5n + 5n + -2n2 + 2n2 Combine like terms: -5n + 5n = 0 -6 + 5n + 1n2 = 0 + -2n2 + 2n2 -6 + 5n + 1n2 = -2n2 + 2n2 Combine like terms: -2n2 + 2n2 = 0 -6 + 5n + 1n2 = 0 Factor a trinomial. (-6 + -1n)(1 + -1n) = 0Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-6, 1}
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