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Simplifying (2n + 5)(n + -1) = 0 Reorder the terms: (5 + 2n)(n + -1) = 0 Reorder the terms: (5 + 2n)(-1 + n) = 0 Multiply (5 + 2n) * (-1 + n) (5(-1 + n) + 2n * (-1 + n)) = 0 ((-1 * 5 + n * 5) + 2n * (-1 + n)) = 0 ((-5 + 5n) + 2n * (-1 + n)) = 0 (-5 + 5n + (-1 * 2n + n * 2n)) = 0 (-5 + 5n + (-2n + 2n2)) = 0 Combine like terms: 5n + -2n = 3n (-5 + 3n + 2n2) = 0 Solving -5 + 3n + 2n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -2n)(1 + -1n) = 0Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 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 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-2.5, 1}
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