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Simplifying -4n2 + 4n + 11 = -5n2 + 8 Reorder the terms: 11 + 4n + -4n2 = -5n2 + 8 Reorder the terms: 11 + 4n + -4n2 = 8 + -5n2 Solving 11 + 4n + -4n2 = 8 + -5n2 Solving for variable 'n'. Reorder the terms: 11 + -8 + 4n + -4n2 + 5n2 = 8 + -5n2 + -8 + 5n2 Combine like terms: 11 + -8 = 3 3 + 4n + -4n2 + 5n2 = 8 + -5n2 + -8 + 5n2 Combine like terms: -4n2 + 5n2 = 1n2 3 + 4n + 1n2 = 8 + -5n2 + -8 + 5n2 Reorder the terms: 3 + 4n + 1n2 = 8 + -8 + -5n2 + 5n2 Combine like terms: 8 + -8 = 0 3 + 4n + 1n2 = 0 + -5n2 + 5n2 3 + 4n + 1n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 3 + 4n + 1n2 = 0 Factor a trinomial. (3 + n)(1 + n) = 0Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {-3, -1}
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