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Simplifying (2n + -5)(5n + -2) = 0 Reorder the terms: (-5 + 2n)(5n + -2) = 0 Reorder the terms: (-5 + 2n)(-2 + 5n) = 0 Multiply (-5 + 2n) * (-2 + 5n) (-5(-2 + 5n) + 2n * (-2 + 5n)) = 0 ((-2 * -5 + 5n * -5) + 2n * (-2 + 5n)) = 0 ((10 + -25n) + 2n * (-2 + 5n)) = 0 (10 + -25n + (-2 * 2n + 5n * 2n)) = 0 (10 + -25n + (-4n + 10n2)) = 0 Combine like terms: -25n + -4n = -29n (10 + -29n + 10n2) = 0 Solving 10 + -29n + 10n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + -5n)(5 + -2n) = 0Subproblem 1
Set the factor '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4Subproblem 2
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 = 2.5Solution
n = {0.4, 2.5}
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