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Simplifying 4n2 = 20 + 2n Solving 4n2 = 20 + 2n Solving for variable 'n'. Reorder the terms: -20 + -2n + 4n2 = 20 + 2n + -20 + -2n Reorder the terms: -20 + -2n + 4n2 = 20 + -20 + 2n + -2n Combine like terms: 20 + -20 = 0 -20 + -2n + 4n2 = 0 + 2n + -2n -20 + -2n + 4n2 = 2n + -2n Combine like terms: 2n + -2n = 0 -20 + -2n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -1n + 2n2) = 0 Factor a trinomial. 2((-2 + -1n)(5 + -2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 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 = {-2, 2.5}
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