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Simplifying (2n + -15)(5n + 8) = 0 Reorder the terms: (-15 + 2n)(5n + 8) = 0 Reorder the terms: (-15 + 2n)(8 + 5n) = 0 Multiply (-15 + 2n) * (8 + 5n) (-15(8 + 5n) + 2n * (8 + 5n)) = 0 ((8 * -15 + 5n * -15) + 2n * (8 + 5n)) = 0 ((-120 + -75n) + 2n * (8 + 5n)) = 0 (-120 + -75n + (8 * 2n + 5n * 2n)) = 0 (-120 + -75n + (16n + 10n2)) = 0 Combine like terms: -75n + 16n = -59n (-120 + -59n + 10n2) = 0 Solving -120 + -59n + 10n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -5n)(15 + -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 '(15 + -2n)' equal to zero and attempt to solve: Simplifying 15 + -2n = 0 Solving 15 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2n = 0 + -15 -2n = 0 + -15 Combine like terms: 0 + -15 = -15 -2n = -15 Divide each side by '-2'. n = 7.5 Simplifying n = 7.5Solution
n = {-1.6, 7.5}
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