3x^2(x^2+2)=20-x^2

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

Simplifying
3x2(x2 + 2) = 20 + -1x2

Reorder the terms:
3x2(2 + x2) = 20 + -1x2
(2 * 3x2 + x2 * 3x2) = 20 + -1x2
(6x2 + 3x4) = 20 + -1x2

Solving
6x2 + 3x4 = 20 + -1x2

Solving for variable 'x'.

Reorder the terms:
-20 + 6x2 + x2 + 3x4 = 20 + -1x2 + -20 + x2

Combine like terms: 6x2 + x2 = 7x2
-20 + 7x2 + 3x4 = 20 + -1x2 + -20 + x2

Reorder the terms:
-20 + 7x2 + 3x4 = 20 + -20 + -1x2 + x2

Combine like terms: 20 + -20 = 0
-20 + 7x2 + 3x4 = 0 + -1x2 + x2
-20 + 7x2 + 3x4 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-20 + 7x2 + 3x4 = 0

Factor a trinomial.
(-4 + -1x2)(5 + -3x2) = 0

Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

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 '(5 + -3x2)' equal to zero and attempt to solve:

Simplifying
5 + -3x2 = 0

Solving
5 + -3x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x2 = 0 + -5
-3x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3x2 = -5

Divide each side by '-3'.
x2 = 1.666666667

Simplifying
x2 = 1.666666667

Take the square root of each side:
x = {-1.290994449, 1.290994449}
Solution
x = {-1.290994449, 1.290994449}