x^2(x^2+1)-3(2x^2+1)+9=0

Solution for x^2(x^2+1)-3(2x^2+1)+9=0 equation:

Simplifying
x2(x2 + 1) + -3(2x2 + 1) + 9 = 0

Reorder the terms:
x2(1 + x2) + -3(2x2 + 1) + 9 = 0
(1 * x2 + x2 * x2) + -3(2x2 + 1) + 9 = 0
(1x2 + x4) + -3(2x2 + 1) + 9 = 0

Reorder the terms:
1x2 + x4 + -3(1 + 2x2) + 9 = 0
1x2 + x4 + (1 * -3 + 2x2 * -3) + 9 = 0
1x2 + x4 + (-3 + -6x2) + 9 = 0

Reorder the terms:
-3 + 9 + 1x2 + -6x2 + x4 = 0

Combine like terms: -3 + 9 = 6
6 + 1x2 + -6x2 + x4 = 0

Combine like terms: 1x2 + -6x2 = -5x2
6 + -5x2 + x4 = 0

Solving
6 + -5x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.414213562, 1.414213562, -1.732050808, 1.732050808}