24x^4+48x^2+96x^6=

Solution for 24x^4+48x^2+96x^6= equation:

Simplifying
24x4 + 48x2 + 96x6 = 0

Reorder the terms:
48x2 + 24x4 + 96x6 = 0

Solving
48x2 + 24x4 + 96x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24x2'.
24x2(2 + x2 + 4x4) = 0

Ignore the factor 24.
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 '(2 + x2 + 4x4)' equal to zero and attempt to solve:

Simplifying
2 + x2 + 4x4 = 0

Solving
2 + x2 + 4x4 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.5 + 0.25x2 + x4 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.25x2 + -0.5 + x4 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.25x2 + x4 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.25x2 + x4 = 0 + -0.5
0.25x2 + x4 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.25x2 + x4 = -0.5

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x2 + 0.25 + x4 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.25x2 + x4 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.25x2 + x4 = -0.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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