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Simplifying 108n4 + -180n2 + 75 = 0 Reorder the terms: 75 + -180n2 + 108n4 = 0 Solving 75 + -180n2 + 108n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -60n2 + 36n4) = 0 Factor a trinomial. 3((5 + -6n2)(5 + -6n2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -6n2)' equal to zero and attempt to solve: Simplifying 5 + -6n2 = 0 Solving 5 + -6n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6n2 = 0 + -5 -6n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6n2 = -5 Divide each side by '-6'. n2 = 0.8333333333 Simplifying n2 = 0.8333333333 Take the square root of each side: n = {-0.912870929, 0.912870929}Subproblem 2
Set the factor '(5 + -6n2)' equal to zero and attempt to solve: Simplifying 5 + -6n2 = 0 Solving 5 + -6n2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6n2 = 0 + -5 -6n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6n2 = -5 Divide each side by '-6'. n2 = 0.8333333333 Simplifying n2 = 0.8333333333 Take the square root of each side: n = {-0.912870929, 0.912870929}Solution
n = {-0.912870929, 0.912870929, -0.912870929, 0.912870929}
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