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Simplifying (6n + 7)(4n + -5) = 0 Reorder the terms: (7 + 6n)(4n + -5) = 0 Reorder the terms: (7 + 6n)(-5 + 4n) = 0 Multiply (7 + 6n) * (-5 + 4n) (7(-5 + 4n) + 6n * (-5 + 4n)) = 0 ((-5 * 7 + 4n * 7) + 6n * (-5 + 4n)) = 0 ((-35 + 28n) + 6n * (-5 + 4n)) = 0 (-35 + 28n + (-5 * 6n + 4n * 6n)) = 0 (-35 + 28n + (-30n + 24n2)) = 0 Combine like terms: 28n + -30n = -2n (-35 + -2n + 24n2) = 0 Solving -35 + -2n + 24n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -6n)(5 + -4n) = 0Subproblem 1
Set the factor '(-7 + -6n)' equal to zero and attempt to solve: Simplifying -7 + -6n = 0 Solving -7 + -6n = 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 + -6n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6n = 0 + 7 -6n = 0 + 7 Combine like terms: 0 + 7 = 7 -6n = 7 Divide each side by '-6'. n = -1.166666667 Simplifying n = -1.166666667Subproblem 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 = {-1.166666667, 1.25}
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