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

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

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

Reorder the terms:
3x2(3 + x2) = 20 + -2x2
(3 * 3x2 + x2 * 3x2) = 20 + -2x2
(9x2 + 3x4) = 20 + -2x2

Solving
9x2 + 3x4 = 20 + -2x2

Solving for variable 'x'.

Reorder the terms:
-20 + 9x2 + 2x2 + 3x4 = 20 + -2x2 + -20 + 2x2

Combine like terms: 9x2 + 2x2 = 11x2
-20 + 11x2 + 3x4 = 20 + -2x2 + -20 + 2x2

Reorder the terms:
-20 + 11x2 + 3x4 = 20 + -20 + -2x2 + 2x2

Combine like terms: 20 + -20 = 0
-20 + 11x2 + 3x4 = 0 + -2x2 + 2x2
-20 + 11x2 + 3x4 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-20 + 11x2 + 3x4 = 0

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

Subproblem 1
Set the factor '(-5 + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + -1x2 = 0

Solving
-5 + -1x2 = 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 + -1x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x2 = 0 + 5
-1x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1x2 = 5

Divide each side by '-1'.
x2 = -5

Simplifying
x2 = -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 + -3x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x2 = 0

Solving
4 + -3x2 = 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 + -3x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x2 = 0 + -4
-3x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3x2 = -4

Divide each side by '-3'.
x2 = 1.333333333

Simplifying
x2 = 1.333333333

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