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