(x^2+1)(x^2+3)=32-4x^2(x^2+5)

Solution for (x^2+1)(x^2+3)=32-4x^2(x^2+5) equation:

Simplifying
(x2 + 1)(x2 + 3) = 32 + -4x2(x2 + 5)

Reorder the terms:
(1 + x2)(x2 + 3) = 32 + -4x2(x2 + 5)

Reorder the terms:
(1 + x2)(3 + x2) = 32 + -4x2(x2 + 5)

Multiply (1 + x2) * (3 + x2)
(1(3 + x2) + x2(3 + x2)) = 32 + -4x2(x2 + 5)
((3 * 1 + x2 * 1) + x2(3 + x2)) = 32 + -4x2(x2 + 5)
((3 + 1x2) + x2(3 + x2)) = 32 + -4x2(x2 + 5)
(3 + 1x2 + (3 * x2 + x2 * x2)) = 32 + -4x2(x2 + 5)
(3 + 1x2 + (3x2 + x4)) = 32 + -4x2(x2 + 5)

Combine like terms: 1x2 + 3x2 = 4x2
(3 + 4x2 + x4) = 32 + -4x2(x2 + 5)

Reorder the terms:
3 + 4x2 + x4 = 32 + -4x2(5 + x2)
3 + 4x2 + x4 = 32 + (5 * -4x2 + x2 * -4x2)
3 + 4x2 + x4 = 32 + (-20x2 + -4x4)

Solving
3 + 4x2 + x4 = 32 + -20x2 + -4x4

Solving for variable 'x'.

Reorder the terms:
3 + -32 + 4x2 + 20x2 + x4 + 4x4 = 32 + -20x2 + -4x4 + -32 + 20x2 + 4x4

Combine like terms: 3 + -32 = -29
-29 + 4x2 + 20x2 + x4 + 4x4 = 32 + -20x2 + -4x4 + -32 + 20x2 + 4x4

Combine like terms: 4x2 + 20x2 = 24x2
-29 + 24x2 + x4 + 4x4 = 32 + -20x2 + -4x4 + -32 + 20x2 + 4x4

Combine like terms: x4 + 4x4 = 5x4
-29 + 24x2 + 5x4 = 32 + -20x2 + -4x4 + -32 + 20x2 + 4x4

Reorder the terms:
-29 + 24x2 + 5x4 = 32 + -32 + -20x2 + 20x2 + -4x4 + 4x4

Combine like terms: 32 + -32 = 0
-29 + 24x2 + 5x4 = 0 + -20x2 + 20x2 + -4x4 + 4x4
-29 + 24x2 + 5x4 = -20x2 + 20x2 + -4x4 + 4x4

Combine like terms: -20x2 + 20x2 = 0
-29 + 24x2 + 5x4 = 0 + -4x4 + 4x4
-29 + 24x2 + 5x4 = -4x4 + 4x4

Combine like terms: -4x4 + 4x4 = 0
-29 + 24x2 + 5x4 = 0

Factor a trinomial.
(-29 + -5x2)(1 + -1x2) = 0

Factor a difference between two squares.
(-29 + -5x2)((1 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor '(-29 + -5x2)' equal to zero and attempt to solve:

Simplifying
-29 + -5x2 = 0

Solving
-29 + -5x2 = 0

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

Add '29' to each side of the equation.
-29 + 29 + -5x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -5x2 = 0 + 29
-5x2 = 0 + 29

Combine like terms: 0 + 29 = 29
-5x2 = 29

Divide each side by '-5'.
x2 = -5.8

Simplifying
x2 = -5.8

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1, 1}