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

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


Simplifying
(3x4y2 + 2x2y4) + -1(6x4y2 + -4x2y4) = 0

Reorder the terms:
(2x2y4 + 3x4y2) + -1(6x4y2 + -4x2y4) = 0

Remove parenthesis around (2x2y4 + 3x4y2)
2x2y4 + 3x4y2 + -1(6x4y2 + -4x2y4) = 0

Reorder the terms:
2x2y4 + 3x4y2 + -1(-4x2y4 + 6x4y2) = 0
2x2y4 + 3x4y2 + (-4x2y4 * -1 + 6x4y2 * -1) = 0
2x2y4 + 3x4y2 + (4x2y4 + -6x4y2) = 0

Reorder the terms:
2x2y4 + 4x2y4 + 3x4y2 + -6x4y2 = 0

Combine like terms: 2x2y4 + 4x2y4 = 6x2y4
6x2y4 + 3x4y2 + -6x4y2 = 0

Combine like terms: 3x4y2 + -6x4y2 = -3x4y2
6x2y4 + -3x4y2 = 0

Solving
6x2y4 + -3x4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2y2'.
3x2y2(2y2 + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2y2' equal to zero and attempt to solve:

Simplifying
x2y2 = 0

Solving
x2y2 = 0

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

Simplifying
x2y2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2y2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2y2 + -1x2 = 0

Reorder the terms:
-1x2 + 2y2 = 0

Solving
-1x2 + 2y2 = 0

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

Add '-2y2' to each side of the equation.
-1x2 + 2y2 + -2y2 = 0 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-1x2 + 0 = 0 + -2y2
-1x2 = 0 + -2y2
Remove the zero:
-1x2 = -2y2

Divide each side by '-1'.
x2 = 2y2

Simplifying
x2 = 2y2

Take the square root of each side:
x = {-1.414213562y, 1.414213562y}
Solution
x = {-1.414213562y, 1.414213562y}

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