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Simplifying (3n + 7)(4n + -1) = 0 Reorder the terms: (7 + 3n)(4n + -1) = 0 Reorder the terms: (7 + 3n)(-1 + 4n) = 0 Multiply (7 + 3n) * (-1 + 4n) (7(-1 + 4n) + 3n * (-1 + 4n)) = 0 ((-1 * 7 + 4n * 7) + 3n * (-1 + 4n)) = 0 ((-7 + 28n) + 3n * (-1 + 4n)) = 0 (-7 + 28n + (-1 * 3n + 4n * 3n)) = 0 (-7 + 28n + (-3n + 12n2)) = 0 Combine like terms: 28n + -3n = 25n (-7 + 25n + 12n2) = 0 Solving -7 + 25n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (-7 + -3n)(1 + -4n) = 0Subproblem 1
Set the factor '(-7 + -3n)' equal to zero and attempt to solve: Simplifying -7 + -3n = 0 Solving -7 + -3n = 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 + -3n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3n = 0 + 7 -3n = 0 + 7 Combine like terms: 0 + 7 = 7 -3n = 7 Divide each side by '-3'. n = -2.333333333 Simplifying n = -2.333333333Subproblem 2
Set the factor '(1 + -4n)' equal to zero and attempt to solve: Simplifying 1 + -4n = 0 Solving 1 + -4n = 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 + -4n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4n = 0 + -1 -4n = 0 + -1 Combine like terms: 0 + -1 = -1 -4n = -1 Divide each side by '-4'. n = 0.25 Simplifying n = 0.25Solution
n = {-2.333333333, 0.25}
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