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Simplifying (n + -5)(5n + -7) = 0 Reorder the terms: (-5 + n)(5n + -7) = 0 Reorder the terms: (-5 + n)(-7 + 5n) = 0 Multiply (-5 + n) * (-7 + 5n) (-5(-7 + 5n) + n(-7 + 5n)) = 0 ((-7 * -5 + 5n * -5) + n(-7 + 5n)) = 0 ((35 + -25n) + n(-7 + 5n)) = 0 (35 + -25n + (-7 * n + 5n * n)) = 0 (35 + -25n + (-7n + 5n2)) = 0 Combine like terms: -25n + -7n = -32n (35 + -32n + 5n2) = 0 Solving 35 + -32n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (7 + -5n)(5 + -1n) = 0Subproblem 1
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 = 1.4Subproblem 2
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 = 5Solution
n = {1.4, 5}
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