(16x^6-12x^4+x^2)=4x^2

Solution for (16x^6-12x^4+x^2)=4x^2 equation:

Simplifying
(16x6 + -12x4 + x2) = 4x2

Reorder the terms:
(x2 + -12x4 + 16x6) = 4x2

Remove parenthesis around (x2 + -12x4 + 16x6)
x2 + -12x4 + 16x6 = 4x2

Solving
x2 + -12x4 + 16x6 = 4x2

Solving for variable 'x'.

Reorder the terms:
x2 + -4x2 + -12x4 + 16x6 = 4x2 + -4x2

Combine like terms: x2 + -4x2 = -3x2
-3x2 + -12x4 + 16x6 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3x2 + -12x4 + 16x6 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + -12x2 + 16x4) = 0

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 '(-3 + -12x2 + 16x4)' equal to zero and attempt to solve:

Simplifying
-3 + -12x2 + 16x4 = 0

Solving
-3 + -12x2 + 16x4 = 0

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

Divide each side by '16'.
-0.1875 + -0.75x2 + x4 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -0.75x2 + 0.1875 + x4 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -0.75x2 + x4 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -0.75x2 + x4 = 0 + 0.1875
-0.75x2 + x4 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-0.75x2 + x4 = 0.1875

The x term is -0.75x2.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x2 + 0.140625 + x4 = 0.1875 + 0.140625

Reorder the terms:
0.140625 + -0.75x2 + x4 = 0.1875 + 0.140625

Combine like terms: 0.1875 + 0.140625 = 0.328125
0.140625 + -0.75x2 + x4 = 0.328125

Factor a perfect square on the left side:
(x2 + -0.375)(x2 + -0.375) = 0.328125

Calculate the square root of the right side: 0.572821962

Break this problem into two subproblems by setting 
(x2 + -0.375) equal to 0.572821962 and -0.572821962.

Subproblem 1
x2 + -0.375 = 0.572821962

Simplifying
x2 + -0.375 = 0.572821962

Reorder the terms:
-0.375 + x2 = 0.572821962

Solving
-0.375 + x2 = 0.572821962

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x2 = 0.572821962 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = 0.572821962 + 0.375
x2 = 0.572821962 + 0.375

Combine like terms: 0.572821962 + 0.375 = 0.947821962
x2 = 0.947821962

Simplifying
x2 = 0.947821962

Take the square root of each side:
x = {-0.973561483, 0.973561483}

Subproblem 2
x2 + -0.375 = -0.572821962

Simplifying
x2 + -0.375 = -0.572821962

Reorder the terms:
-0.375 + x2 = -0.572821962

Solving
-0.375 + x2 = -0.572821962

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x2 = -0.572821962 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = -0.572821962 + 0.375
x2 = -0.572821962 + 0.375

Combine like terms: -0.572821962 + 0.375 = -0.197821962
x2 = -0.197821962

Simplifying
x2 = -0.197821962

Reorder the terms:
0.197821962 + x2 = -0.197821962 + 0.197821962

Combine like terms: -0.197821962 + 0.197821962 = 0.000000000
0.197821962 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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