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Simplifying (5n + -7)(n + 5) = 0 Reorder the terms: (-7 + 5n)(n + 5) = 0 Reorder the terms: (-7 + 5n)(5 + n) = 0 Multiply (-7 + 5n) * (5 + n) (-7(5 + n) + 5n * (5 + n)) = 0 ((5 * -7 + n * -7) + 5n * (5 + n)) = 0 ((-35 + -7n) + 5n * (5 + n)) = 0 (-35 + -7n + (5 * 5n + n * 5n)) = 0 (-35 + -7n + (25n + 5n2)) = 0 Combine like terms: -7n + 25n = 18n (-35 + 18n + 5n2) = 0 Solving -35 + 18n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -1n)(7 + -5n) = 0Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 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 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5Subproblem 2
Set the factor '(7 + -5n)' equal to zero and attempt to solve: Simplifying 7 + -5n = 0 Solving 7 + -5n = 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 + -5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5n = 0 + -7 -5n = 0 + -7 Combine like terms: 0 + -7 = -7 -5n = -7 Divide each side by '-5'. n = 1.4 Simplifying n = 1.4Solution
n = {-5, 1.4}
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