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Simplifying 12n3 = 3n Solving 12n3 = 3n Solving for variable 'n'. Reorder the terms: -3n + 12n3 = 3n + -3n Combine like terms: 3n + -3n = 0 -3n + 12n3 = 0 Factor out the Greatest Common Factor (GCF), '3n'. 3n(-1 + 4n2) = 0 Factor a difference between two squares. 3n((1 + 2n)(-1 + 2n)) = 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 '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Subproblem 3
Set the factor '(-1 + 2n)' equal to zero and attempt to solve: Simplifying -1 + 2n = 0 Solving -1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2n = 0 + 1 2n = 0 + 1 Combine like terms: 0 + 1 = 1 2n = 1 Divide each side by '2'. n = 0.5 Simplifying n = 0.5Solution
n = {0, -0.5, 0.5}
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