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Simplifying (5n + -2)(2n + -7) = 0 Reorder the terms: (-2 + 5n)(2n + -7) = 0 Reorder the terms: (-2 + 5n)(-7 + 2n) = 0 Multiply (-2 + 5n) * (-7 + 2n) (-2(-7 + 2n) + 5n * (-7 + 2n)) = 0 ((-7 * -2 + 2n * -2) + 5n * (-7 + 2n)) = 0 ((14 + -4n) + 5n * (-7 + 2n)) = 0 (14 + -4n + (-7 * 5n + 2n * 5n)) = 0 (14 + -4n + (-35n + 10n2)) = 0 Combine like terms: -4n + -35n = -39n (14 + -39n + 10n2) = 0 Solving 14 + -39n + 10n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + -5n)(7 + -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 '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 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 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Solution
n = {0.4, 3.5}
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