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Simplifying 8n3 = 18n Solving 8n3 = 18n Solving for variable 'n'. Reorder the terms: -18n + 8n3 = 18n + -18n Combine like terms: 18n + -18n = 0 -18n + 8n3 = 0 Factor out the Greatest Common Factor (GCF), '2n'. 2n(-9 + 4n2) = 0 Factor a difference between two squares. 2n((3 + 2n)(-3 + 2n)) = 0 Ignore the factor 2.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 '(3 + 2n)' equal to zero and attempt to solve: Simplifying 3 + 2n = 0 Solving 3 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = 0 + -3 2n = 0 + -3 Combine like terms: 0 + -3 = -3 2n = -3 Divide each side by '2'. n = -1.5 Simplifying n = -1.5Subproblem 3
Set the factor '(-3 + 2n)' equal to zero and attempt to solve: Simplifying -3 + 2n = 0 Solving -3 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2n = 0 + 3 2n = 0 + 3 Combine like terms: 0 + 3 = 3 2n = 3 Divide each side by '2'. n = 1.5 Simplifying n = 1.5Solution
n = {0, -1.5, 1.5}
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