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Simplifying (3n + 7)(3n + -5) = -2n(5n + 2) + -26 Reorder the terms: (7 + 3n)(3n + -5) = -2n(5n + 2) + -26 Reorder the terms: (7 + 3n)(-5 + 3n) = -2n(5n + 2) + -26 Multiply (7 + 3n) * (-5 + 3n) (7(-5 + 3n) + 3n * (-5 + 3n)) = -2n(5n + 2) + -26 ((-5 * 7 + 3n * 7) + 3n * (-5 + 3n)) = -2n(5n + 2) + -26 ((-35 + 21n) + 3n * (-5 + 3n)) = -2n(5n + 2) + -26 (-35 + 21n + (-5 * 3n + 3n * 3n)) = -2n(5n + 2) + -26 (-35 + 21n + (-15n + 9n2)) = -2n(5n + 2) + -26 Combine like terms: 21n + -15n = 6n (-35 + 6n + 9n2) = -2n(5n + 2) + -26 Reorder the terms: -35 + 6n + 9n2 = -2n(2 + 5n) + -26 -35 + 6n + 9n2 = (2 * -2n + 5n * -2n) + -26 -35 + 6n + 9n2 = (-4n + -10n2) + -26 Reorder the terms: -35 + 6n + 9n2 = -26 + -4n + -10n2 Solving -35 + 6n + 9n2 = -26 + -4n + -10n2 Solving for variable 'n'. Reorder the terms: -35 + 26 + 6n + 4n + 9n2 + 10n2 = -26 + -4n + -10n2 + 26 + 4n + 10n2 Combine like terms: -35 + 26 = -9 -9 + 6n + 4n + 9n2 + 10n2 = -26 + -4n + -10n2 + 26 + 4n + 10n2 Combine like terms: 6n + 4n = 10n -9 + 10n + 9n2 + 10n2 = -26 + -4n + -10n2 + 26 + 4n + 10n2 Combine like terms: 9n2 + 10n2 = 19n2 -9 + 10n + 19n2 = -26 + -4n + -10n2 + 26 + 4n + 10n2 Reorder the terms: -9 + 10n + 19n2 = -26 + 26 + -4n + 4n + -10n2 + 10n2 Combine like terms: -26 + 26 = 0 -9 + 10n + 19n2 = 0 + -4n + 4n + -10n2 + 10n2 -9 + 10n + 19n2 = -4n + 4n + -10n2 + 10n2 Combine like terms: -4n + 4n = 0 -9 + 10n + 19n2 = 0 + -10n2 + 10n2 -9 + 10n + 19n2 = -10n2 + 10n2 Combine like terms: -10n2 + 10n2 = 0 -9 + 10n + 19n2 = 0 Factor a trinomial. (-1 + -1n)(9 + -19n) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(9 + -19n)' equal to zero and attempt to solve: Simplifying 9 + -19n = 0 Solving 9 + -19n = 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 + -19n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -19n = 0 + -9 -19n = 0 + -9 Combine like terms: 0 + -9 = -9 -19n = -9 Divide each side by '-19'. n = 0.4736842105 Simplifying n = 0.4736842105Solution
n = {-1, 0.4736842105}
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