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Simplifying 0 = 2(n3 + 4n2) Reorder the terms: 0 = 2(4n2 + n3) 0 = (4n2 * 2 + n3 * 2) 0 = (8n2 + 2n3) Solving 0 = 8n2 + 2n3 Solving for variable 'n'. Remove the zero: -8n2 + -2n3 = 8n2 + 2n3 + -8n2 + -2n3 Reorder the terms: -8n2 + -2n3 = 8n2 + -8n2 + 2n3 + -2n3 Combine like terms: 8n2 + -8n2 = 0 -8n2 + -2n3 = 0 + 2n3 + -2n3 -8n2 + -2n3 = 2n3 + -2n3 Combine like terms: 2n3 + -2n3 = 0 -8n2 + -2n3 = 0 Factor out the Greatest Common Factor (GCF), '-2n2'. -2n2(4 + n) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 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 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4Solution
n = {0, -4}
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