(-3x^6+3x^4-x^2)-(-x^6+2x^4+2x^2)=

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Solution for (-3x^6+3x^4-x^2)-(-x^6+2x^4+2x^2)= equation: 


Simplifying
(-3x6 + 3x4 + -1x2) + -1(-1x6 + 2x4 + 2x2) = 0

Reorder the terms:
(-1x2 + 3x4 + -3x6) + -1(-1x6 + 2x4 + 2x2) = 0

Remove parenthesis around (-1x2 + 3x4 + -3x6)
-1x2 + 3x4 + -3x6 + -1(-1x6 + 2x4 + 2x2) = 0

Reorder the terms:
-1x2 + 3x4 + -3x6 + -1(2x2 + 2x4 + -1x6) = 0
-1x2 + 3x4 + -3x6 + (2x2 * -1 + 2x4 * -1 + -1x6 * -1) = 0
-1x2 + 3x4 + -3x6 + (-2x2 + -2x4 + 1x6) = 0

Reorder the terms:
-1x2 + -2x2 + 3x4 + -2x4 + -3x6 + 1x6 = 0

Combine like terms: -1x2 + -2x2 = -3x2
-3x2 + 3x4 + -2x4 + -3x6 + 1x6 = 0

Combine like terms: 3x4 + -2x4 = 1x4
-3x2 + 1x4 + -3x6 + 1x6 = 0

Combine like terms: -3x6 + 1x6 = -2x6
-3x2 + 1x4 + -2x6 = 0

Solving
-3x2 + 1x4 + -2x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + x2 + -2x4) = 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 + x2 + -2x4)' equal to zero and attempt to solve:

Simplifying
-3 + x2 + -2x4 = 0

Solving
-3 + x2 + -2x4 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -0.5x2 + x4 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5x2 + -1.5 + x4 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5x2 + x4 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5x2 + x4 = 0 + -1.5
-0.5x2 + x4 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5x2 + x4 = -1.5

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.
-0.5x2 + 0.25 + x4 = -1.5 + 0.25

Reorder the terms:
0.25 + -0.5x2 + x4 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -0.5x2 + x4 = -1.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = -1.25

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}

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