(7x^4y^2+4x^2Y^3)-(5x^4y^2-2x^2y^3)=

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Solution for (7x^4y^2+4x^2Y^3)-(5x^4y^2-2x^2y^3)= equation: 


Simplifying
(7x4y2 + 4x2Y3) + -1(5x4y2 + -2x2y3) = 0

Reorder the terms:
(4x2Y3 + 7x4y2) + -1(5x4y2 + -2x2y3) = 0

Remove parenthesis around (4x2Y3 + 7x4y2)
4x2Y3 + 7x4y2 + -1(5x4y2 + -2x2y3) = 0

Reorder the terms:
4x2Y3 + 7x4y2 + -1(-2x2y3 + 5x4y2) = 0
4x2Y3 + 7x4y2 + (-2x2y3 * -1 + 5x4y2 * -1) = 0
4x2Y3 + 7x4y2 + (2x2y3 + -5x4y2) = 0

Reorder the terms:
4x2Y3 + 2x2y3 + 7x4y2 + -5x4y2 = 0

Combine like terms: 7x4y2 + -5x4y2 = 2x4y2
4x2Y3 + 2x2y3 + 2x4y2 = 0

Solving
4x2Y3 + 2x2y3 + 2x4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(2Y3 + y3 + x2y2) = 0

Ignore the factor 2.

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 '(2Y3 + y3 + x2y2)' equal to zero and attempt to solve:

Simplifying
2Y3 + y3 + x2y2 = 0

Reorder the terms:
2Y3 + x2y2 + y3 = 0

Solving
2Y3 + x2y2 + y3 = 0

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

Add '-2Y3' to each side of the equation.
2Y3 + x2y2 + -2Y3 + y3 = 0 + -2Y3

Reorder the terms:
2Y3 + -2Y3 + x2y2 + y3 = 0 + -2Y3

Combine like terms: 2Y3 + -2Y3 = 0
0 + x2y2 + y3 = 0 + -2Y3
x2y2 + y3 = 0 + -2Y3
Remove the zero:
x2y2 + y3 = -2Y3

Add '-1y3' to each side of the equation.
x2y2 + y3 + -1y3 = -2Y3 + -1y3

Combine like terms: y3 + -1y3 = 0
x2y2 + 0 = -2Y3 + -1y3
x2y2 = -2Y3 + -1y3

Divide each side by 'y2'.
x2 = -2y-2Y3 + -1y

Simplifying
x2 = -2y-2Y3 + -1y

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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