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Simplifying (3n + 5)(6n + -8) = 0 Reorder the terms: (5 + 3n)(6n + -8) = 0 Reorder the terms: (5 + 3n)(-8 + 6n) = 0 Multiply (5 + 3n) * (-8 + 6n) (5(-8 + 6n) + 3n * (-8 + 6n)) = 0 ((-8 * 5 + 6n * 5) + 3n * (-8 + 6n)) = 0 ((-40 + 30n) + 3n * (-8 + 6n)) = 0 (-40 + 30n + (-8 * 3n + 6n * 3n)) = 0 (-40 + 30n + (-24n + 18n2)) = 0 Combine like terms: 30n + -24n = 6n (-40 + 6n + 18n2) = 0 Solving -40 + 6n + 18n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 3n + 9n2) = 0 Factor a trinomial. 2((-5 + -3n)(4 + -3n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve: Simplifying -5 + -3n = 0 Solving -5 + -3n = 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 + -3n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3n = 0 + 5 -3n = 0 + 5 Combine like terms: 0 + 5 = 5 -3n = 5 Divide each side by '-3'. n = -1.666666667 Simplifying n = -1.666666667Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {-1.666666667, 1.333333333}
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