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Simplifying 50n2 = -65n + -20 Reorder the terms: 50n2 = -20 + -65n Solving 50n2 = -20 + -65n Solving for variable 'n'. Reorder the terms: 20 + 65n + 50n2 = -20 + -65n + 20 + 65n Reorder the terms: 20 + 65n + 50n2 = -20 + 20 + -65n + 65n Combine like terms: -20 + 20 = 0 20 + 65n + 50n2 = 0 + -65n + 65n 20 + 65n + 50n2 = -65n + 65n Combine like terms: -65n + 65n = 0 20 + 65n + 50n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + 13n + 10n2) = 0 Factor a trinomial. 5((4 + 5n)(1 + 2n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + 5n)' equal to zero and attempt to solve: Simplifying 4 + 5n = 0 Solving 4 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n = 0 + -4 5n = 0 + -4 Combine like terms: 0 + -4 = -4 5n = -4 Divide each side by '5'. n = -0.8 Simplifying n = -0.8Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 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 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-0.8, -0.5}
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