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Simplifying (5n + 8)(2n + -1) = 0 Reorder the terms: (8 + 5n)(2n + -1) = 0 Reorder the terms: (8 + 5n)(-1 + 2n) = 0 Multiply (8 + 5n) * (-1 + 2n) (8(-1 + 2n) + 5n * (-1 + 2n)) = 0 ((-1 * 8 + 2n * 8) + 5n * (-1 + 2n)) = 0 ((-8 + 16n) + 5n * (-1 + 2n)) = 0 (-8 + 16n + (-1 * 5n + 2n * 5n)) = 0 (-8 + 16n + (-5n + 10n2)) = 0 Combine like terms: 16n + -5n = 11n (-8 + 11n + 10n2) = 0 Solving -8 + 11n + 10n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -5n)(1 + -2n) = 0Subproblem 1
Set the factor '(-8 + -5n)' equal to zero and attempt to solve: Simplifying -8 + -5n = 0 Solving -8 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5n = 0 + 8 -5n = 0 + 8 Combine like terms: 0 + 8 = 8 -5n = 8 Divide each side by '-5'. n = -1.6 Simplifying n = -1.6Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-1.6, 0.5}
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