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Simplifying 17n2 + 2n + -17 = 12n2 + -10n Reorder the terms: -17 + 2n + 17n2 = 12n2 + -10n Reorder the terms: -17 + 2n + 17n2 = -10n + 12n2 Solving -17 + 2n + 17n2 = -10n + 12n2 Solving for variable 'n'. Reorder the terms: -17 + 2n + 10n + 17n2 + -12n2 = -10n + 12n2 + 10n + -12n2 Combine like terms: 2n + 10n = 12n -17 + 12n + 17n2 + -12n2 = -10n + 12n2 + 10n + -12n2 Combine like terms: 17n2 + -12n2 = 5n2 -17 + 12n + 5n2 = -10n + 12n2 + 10n + -12n2 Reorder the terms: -17 + 12n + 5n2 = -10n + 10n + 12n2 + -12n2 Combine like terms: -10n + 10n = 0 -17 + 12n + 5n2 = 0 + 12n2 + -12n2 -17 + 12n + 5n2 = 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 -17 + 12n + 5n2 = 0 Factor a trinomial. (-17 + -5n)(1 + -1n) = 0Subproblem 1
Set the factor '(-17 + -5n)' equal to zero and attempt to solve: Simplifying -17 + -5n = 0 Solving -17 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -5n = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -5n = 0 + 17 -5n = 0 + 17 Combine like terms: 0 + 17 = 17 -5n = 17 Divide each side by '-5'. n = -3.4 Simplifying n = -3.4Subproblem 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 = {-3.4, 1}
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