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Simplifying 27n3 = 48n Solving 27n3 = 48n Solving for variable 'n'. Reorder the terms: -48n + 27n3 = 48n + -48n Combine like terms: 48n + -48n = 0 -48n + 27n3 = 0 Factor out the Greatest Common Factor (GCF), '3n'. 3n(-16 + 9n2) = 0 Factor a difference between two squares. 3n((4 + 3n)(-4 + 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 + 3n)' equal to zero and attempt to solve: Simplifying 4 + 3n = 0 Solving 4 + 3n = 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 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333Subproblem 3
Set the factor '(-4 + 3n)' equal to zero and attempt to solve: Simplifying -4 + 3n = 0 Solving -4 + 3n = 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 + 3n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3n = 0 + 4 3n = 0 + 4 Combine like terms: 0 + 4 = 4 3n = 4 Divide each side by '3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {0, -1.333333333, 1.333333333}
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