(7x^2-6xy)-(4x^2+6yx)+(4x^2y+x^2)=

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Solution for (7x^2-6xy)-(4x^2+6yx)+(4x^2y+x^2)= equation: 


Simplifying
(7x2 + -6xy) + -1(4x2 + 6yx) + (4x2y + x2) = 0

Reorder the terms:
(-6xy + 7x2) + -1(4x2 + 6yx) + (4x2y + x2) = 0

Remove parenthesis around (-6xy + 7x2)
-6xy + 7x2 + -1(4x2 + 6yx) + (4x2y + x2) = 0

Reorder the terms:
-6xy + 7x2 + -1(6xy + 4x2) + (4x2y + x2) = 0
-6xy + 7x2 + (6xy * -1 + 4x2 * -1) + (4x2y + x2) = 0
-6xy + 7x2 + (-6xy + -4x2) + (4x2y + x2) = 0

Reorder the terms:
-6xy + 7x2 + -6xy + -4x2 + (x2 + 4x2y) = 0

Remove parenthesis around (x2 + 4x2y)
-6xy + 7x2 + -6xy + -4x2 + x2 + 4x2y = 0

Reorder the terms:
-6xy + -6xy + 7x2 + -4x2 + x2 + 4x2y = 0

Combine like terms: -6xy + -6xy = -12xy
-12xy + 7x2 + -4x2 + x2 + 4x2y = 0

Combine like terms: 7x2 + -4x2 = 3x2
-12xy + 3x2 + x2 + 4x2y = 0

Combine like terms: 3x2 + x2 = 4x2
-12xy + 4x2 + 4x2y = 0

Solving
-12xy + 4x2 + 4x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-3y + x + xy) = 0

Ignore the factor 4.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-3y + x + xy)' equal to zero and attempt to solve:

Simplifying
-3y + x + xy = 0

Reorder the terms:
x + xy + -3y = 0

Solving
x + xy + -3y = 0

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

Add '3y' to each side of the equation.
x + xy + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
x + xy + 0 = 0 + 3y
x + xy = 0 + 3y
Remove the zero:
x + xy = 3y

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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