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Simplifying (7n + 5)(4n + 5) = 0 Reorder the terms: (5 + 7n)(4n + 5) = 0 Reorder the terms: (5 + 7n)(5 + 4n) = 0 Multiply (5 + 7n) * (5 + 4n) (5(5 + 4n) + 7n * (5 + 4n)) = 0 ((5 * 5 + 4n * 5) + 7n * (5 + 4n)) = 0 ((25 + 20n) + 7n * (5 + 4n)) = 0 (25 + 20n + (5 * 7n + 4n * 7n)) = 0 (25 + 20n + (35n + 28n2)) = 0 Combine like terms: 20n + 35n = 55n (25 + 55n + 28n2) = 0 Solving 25 + 55n + 28n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + 4n)(5 + 7n) = 0Subproblem 1
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 = -1.25Subproblem 2
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 = -0.7142857143Solution
n = {-1.25, -0.7142857143}
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