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Simplifying 20n2 = 96n + 20 Reorder the terms: 20n2 = 20 + 96n Solving 20n2 = 20 + 96n Solving for variable 'n'. Reorder the terms: -20 + -96n + 20n2 = 20 + 96n + -20 + -96n Reorder the terms: -20 + -96n + 20n2 = 20 + -20 + 96n + -96n Combine like terms: 20 + -20 = 0 -20 + -96n + 20n2 = 0 + 96n + -96n -20 + -96n + 20n2 = 96n + -96n Combine like terms: 96n + -96n = 0 -20 + -96n + 20n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -24n + 5n2) = 0 Factor a trinomial. 4((-1 + -5n)(5 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -5n)' equal to zero and attempt to solve: Simplifying -1 + -5n = 0 Solving -1 + -5n = 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 + -5n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5n = 0 + 1 -5n = 0 + 1 Combine like terms: 0 + 1 = 1 -5n = 1 Divide each side by '-5'. n = -0.2 Simplifying n = -0.2Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-0.2, 5}
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