27n^4-90n^2+75=

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Solution for 27n^4-90n^2+75= equation:


Simplifying
27n4 + -90n2 + 75 = 0

Reorder the terms:
75 + -90n2 + 27n4 = 0

Solving
75 + -90n2 + 27n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -30n2 + 9n4) = 0

Factor a trinomial.
3((5 + -3n2)(5 + -3n2)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -3n2)' equal to zero and attempt to solve: Simplifying 5 + -3n2 = 0 Solving 5 + -3n2 = 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 + -3n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n2 = 0 + -5 -3n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3n2 = -5 Divide each side by '-3'. n2 = 1.666666667 Simplifying n2 = 1.666666667 Take the square root of each side: n = {-1.290994449, 1.290994449}

Subproblem 2

Set the factor '(5 + -3n2)' equal to zero and attempt to solve: Simplifying 5 + -3n2 = 0 Solving 5 + -3n2 = 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 + -3n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n2 = 0 + -5 -3n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3n2 = -5 Divide each side by '-3'. n2 = 1.666666667 Simplifying n2 = 1.666666667 Take the square root of each side: n = {-1.290994449, 1.290994449}

Solution

n = {-1.290994449, 1.290994449, -1.290994449, 1.290994449}

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