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Simplifying 40n2 + 185n + 53 = 5n2 + 3 Reorder the terms: 53 + 185n + 40n2 = 5n2 + 3 Reorder the terms: 53 + 185n + 40n2 = 3 + 5n2 Solving 53 + 185n + 40n2 = 3 + 5n2 Solving for variable 'n'. Reorder the terms: 53 + -3 + 185n + 40n2 + -5n2 = 3 + 5n2 + -3 + -5n2 Combine like terms: 53 + -3 = 50 50 + 185n + 40n2 + -5n2 = 3 + 5n2 + -3 + -5n2 Combine like terms: 40n2 + -5n2 = 35n2 50 + 185n + 35n2 = 3 + 5n2 + -3 + -5n2 Reorder the terms: 50 + 185n + 35n2 = 3 + -3 + 5n2 + -5n2 Combine like terms: 3 + -3 = 0 50 + 185n + 35n2 = 0 + 5n2 + -5n2 50 + 185n + 35n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 50 + 185n + 35n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(10 + 37n + 7n2) = 0 Factor a trinomial. 5((5 + n)(2 + 7n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 2
Set the factor '(2 + 7n)' equal to zero and attempt to solve: Simplifying 2 + 7n = 0 Solving 2 + 7n = 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 + 7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7n = 0 + -2 7n = 0 + -2 Combine like terms: 0 + -2 = -2 7n = -2 Divide each side by '7'. n = -0.2857142857 Simplifying n = -0.2857142857Solution
n = {-5, -0.2857142857}
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