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Simplifying (2n + -7)(-4n + -5) = 0 Reorder the terms: (-7 + 2n)(-4n + -5) = 0 Reorder the terms: (-7 + 2n)(-5 + -4n) = 0 Multiply (-7 + 2n) * (-5 + -4n) (-7(-5 + -4n) + 2n * (-5 + -4n)) = 0 ((-5 * -7 + -4n * -7) + 2n * (-5 + -4n)) = 0 ((35 + 28n) + 2n * (-5 + -4n)) = 0 (35 + 28n + (-5 * 2n + -4n * 2n)) = 0 (35 + 28n + (-10n + -8n2)) = 0 Combine like terms: 28n + -10n = 18n (35 + 18n + -8n2) = 0 Solving 35 + 18n + -8n2 = 0 Solving for variable 'n'. Factor a trinomial. (7 + -2n)(5 + 4n) = 0Subproblem 1
Set the factor '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Subproblem 2
Set the factor '(5 + 4n)' equal to zero and attempt to solve: Simplifying 5 + 4n = 0 Solving 5 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4n = 0 + -5 4n = 0 + -5 Combine like terms: 0 + -5 = -5 4n = -5 Divide each side by '4'. n = -1.25 Simplifying n = -1.25Solution
n = {3.5, -1.25}
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