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Simplifying 4n2 + -126 = -5n + 3n2 Reorder the terms: -126 + 4n2 = -5n + 3n2 Solving -126 + 4n2 = -5n + 3n2 Solving for variable 'n'. Reorder the terms: -126 + 5n + 4n2 + -3n2 = -5n + 3n2 + 5n + -3n2 Combine like terms: 4n2 + -3n2 = 1n2 -126 + 5n + 1n2 = -5n + 3n2 + 5n + -3n2 Reorder the terms: -126 + 5n + 1n2 = -5n + 5n + 3n2 + -3n2 Combine like terms: -5n + 5n = 0 -126 + 5n + 1n2 = 0 + 3n2 + -3n2 -126 + 5n + 1n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 -126 + 5n + 1n2 = 0 Factor a trinomial. (-14 + -1n)(9 + -1n) = 0Subproblem 1
Set the factor '(-14 + -1n)' equal to zero and attempt to solve: Simplifying -14 + -1n = 0 Solving -14 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1n = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1n = 0 + 14 -1n = 0 + 14 Combine like terms: 0 + 14 = 14 -1n = 14 Divide each side by '-1'. n = -14 Simplifying n = -14Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 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 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {-14, 9}
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