3n^2(n^2-3)=20-20n^2

Solution for 3n^2(n^2-3)=20-20n^2 equation:

Simplifying
3n2(n2 + -3) = 20 + -20n2

Reorder the terms:
3n2(-3 + n2) = 20 + -20n2
(-3 * 3n2 + n2 * 3n2) = 20 + -20n2
(-9n2 + 3n4) = 20 + -20n2

Solving
-9n2 + 3n4 = 20 + -20n2

Solving for variable 'n'.

Reorder the terms:
-20 + -9n2 + 20n2 + 3n4 = 20 + -20n2 + -20 + 20n2

Combine like terms: -9n2 + 20n2 = 11n2
-20 + 11n2 + 3n4 = 20 + -20n2 + -20 + 20n2

Reorder the terms:
-20 + 11n2 + 3n4 = 20 + -20 + -20n2 + 20n2

Combine like terms: 20 + -20 = 0
-20 + 11n2 + 3n4 = 0 + -20n2 + 20n2
-20 + 11n2 + 3n4 = -20n2 + 20n2

Combine like terms: -20n2 + 20n2 = 0
-20 + 11n2 + 3n4 = 0

Factor a trinomial.
(-5 + -1n2)(4 + -3n2) = 0

Subproblem 1
Set the factor '(-5 + -1n2)' equal to zero and attempt to solve:

Simplifying
-5 + -1n2 = 0

Solving
-5 + -1n2 = 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 + -1n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n2 = 0 + 5
-1n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1n2 = 5

Divide each side by '-1'.
n2 = -5

Simplifying
n2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4 + -3n2)' equal to zero and attempt to solve:

Simplifying
4 + -3n2 = 0

Solving
4 + -3n2 = 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 + -3n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n2 = 0 + -4
-3n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3n2 = -4

Divide each side by '-3'.
n2 = 1.333333333

Simplifying
n2 = 1.333333333

Take the square root of each side:
n = {-1.154700538, 1.154700538}
Solution
n = {-1.154700538, 1.154700538}