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Simplifying 0 = 4n(3n + 5) Reorder the terms: 0 = 4n(5 + 3n) 0 = (5 * 4n + 3n * 4n) 0 = (20n + 12n2) Solving 0 = 20n + 12n2 Solving for variable 'n'. Remove the zero: -20n + -12n2 = 20n + 12n2 + -20n + -12n2 Reorder the terms: -20n + -12n2 = 20n + -20n + 12n2 + -12n2 Combine like terms: 20n + -20n = 0 -20n + -12n2 = 0 + 12n2 + -12n2 -20n + -12n2 = 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 -20n + -12n2 = 0 Factor out the Greatest Common Factor (GCF), '-4n'. -4n(5 + 3n) = 0 Ignore the factor -4.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 '(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, -1.666666667}
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