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Simplifying 63n3 + -69n2 + 20n = 80n Reorder the terms: 20n + -69n2 + 63n3 = 80n Solving 20n + -69n2 + 63n3 = 80n Solving for variable 'n'. Reorder the terms: 20n + -80n + -69n2 + 63n3 = 80n + -80n Combine like terms: 20n + -80n = -60n -60n + -69n2 + 63n3 = 80n + -80n Combine like terms: 80n + -80n = 0 -60n + -69n2 + 63n3 = 0 Factor out the Greatest Common Factor (GCF), '3n'. 3n(-20 + -23n + 21n2) = 0 Factor a trinomial. 3n((-4 + -7n)(5 + -3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-4 + -7n)' equal to zero and attempt to solve: Simplifying -4 + -7n = 0 Solving -4 + -7n = 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 + -7n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7n = 0 + 4 -7n = 0 + 4 Combine like terms: 0 + 4 = 4 -7n = 4 Divide each side by '-7'. n = -0.5714285714 Simplifying n = -0.5714285714Subproblem 3
Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {0, -0.5714285714, 1.666666667}
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