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Simplifying 12n4 + -36n2 + 27 = 0 Reorder the terms: 27 + -36n2 + 12n4 = 0 Solving 27 + -36n2 + 12n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -12n2 + 4n4) = 0 Factor a trinomial. 3((3 + -2n2)(3 + -2n2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2n2)' equal to zero and attempt to solve: Simplifying 3 + -2n2 = 0 Solving 3 + -2n2 = 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 + -2n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n2 = 0 + -3 -2n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2n2 = -3 Divide each side by '-2'. n2 = 1.5 Simplifying n2 = 1.5 Take the square root of each side: n = {-1.224744871, 1.224744871}Subproblem 2
Set the factor '(3 + -2n2)' equal to zero and attempt to solve: Simplifying 3 + -2n2 = 0 Solving 3 + -2n2 = 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 + -2n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n2 = 0 + -3 -2n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2n2 = -3 Divide each side by '-2'. n2 = 1.5 Simplifying n2 = 1.5 Take the square root of each side: n = {-1.224744871, 1.224744871}Solution
n = {-1.224744871, 1.224744871, -1.224744871, 1.224744871}
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