48x^6+88x^4+32x^2=0

Solution for 48x^6+88x^4+32x^2=0 equation:

Simplifying
48x6 + 88x4 + 32x2 = 0

Reorder the terms:
32x2 + 88x4 + 48x6 = 0

Solving
32x2 + 88x4 + 48x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x2'.
8x2(4 + 11x2 + 6x4) = 0

Factor a trinomial.
8x2((4 + 3x2)(1 + 2x2)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 2x2 = 0

Solving
1 + 2x2 = 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 + 2x2 = 0 + -1

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

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

Divide each side by '2'.
x2 = -0.5

Simplifying
x2 = -0.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}