48x^6+54x^4+24x^2=

Solution for 48x^6+54x^4+24x^2= equation:

Simplifying
48x6 + 54x4 + 24x2 = 0

Reorder the terms:
24x2 + 54x4 + 48x6 = 0

Solving
24x2 + 54x4 + 48x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(4 + 9x2 + 8x4) = 0

Ignore the factor 6.
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 + 9x2 + 8x4)' equal to zero and attempt to solve:

Simplifying
4 + 9x2 + 8x4 = 0

Solving
4 + 9x2 + 8x4 = 0

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

Divide each side by '8'.
0.5 + 1.125x2 + x4 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 1.125x2 + -0.5 + x4 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 1.125x2 + x4 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 1.125x2 + x4 = 0 + -0.5
1.125x2 + x4 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
1.125x2 + x4 = -0.5

The x term is 1.125x2.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x2 + 0.31640625 + x4 = -0.5 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x2 + x4 = -0.5 + 0.31640625

Combine like terms: -0.5 + 0.31640625 = -0.18359375
0.31640625 + 1.125x2 + x4 = -0.18359375

Factor a perfect square on the left side:
(x2 + 0.5625)(x2 + 0.5625) = -0.18359375

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}