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Simplifying (7n + 5)(4n + -1) = 0 Reorder the terms: (5 + 7n)(4n + -1) = 0 Reorder the terms: (5 + 7n)(-1 + 4n) = 0 Multiply (5 + 7n) * (-1 + 4n) (5(-1 + 4n) + 7n * (-1 + 4n)) = 0 ((-1 * 5 + 4n * 5) + 7n * (-1 + 4n)) = 0 ((-5 + 20n) + 7n * (-1 + 4n)) = 0 (-5 + 20n + (-1 * 7n + 4n * 7n)) = 0 (-5 + 20n + (-7n + 28n2)) = 0 Combine like terms: 20n + -7n = 13n (-5 + 13n + 28n2) = 0 Solving -5 + 13n + 28n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -7n)(1 + -4n) = 0Subproblem 1
Set the factor '(-5 + -7n)' equal to zero and attempt to solve: Simplifying -5 + -7n = 0 Solving -5 + -7n = 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 + -7n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7n = 0 + 5 -7n = 0 + 5 Combine like terms: 0 + 5 = 5 -7n = 5 Divide each side by '-7'. n = -0.7142857143 Simplifying n = -0.7142857143Subproblem 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 = {-0.7142857143, 0.25}
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