(2x^2-xy+y^2)+(-3x^2+4xy+3y^2)=0

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Solution for (2x^2-xy+y^2)+(-3x^2+4xy+3y^2)=0 equation: 


Simplifying
(2x2 + -1xy + y2) + (-3x2 + 4xy + 3y2) = 0

Reorder the terms:
(-1xy + 2x2 + y2) + (-3x2 + 4xy + 3y2) = 0

Remove parenthesis around (-1xy + 2x2 + y2)
-1xy + 2x2 + y2 + (-3x2 + 4xy + 3y2) = 0

Reorder the terms:
-1xy + 2x2 + y2 + (4xy + -3x2 + 3y2) = 0

Remove parenthesis around (4xy + -3x2 + 3y2)
-1xy + 2x2 + y2 + 4xy + -3x2 + 3y2 = 0

Reorder the terms:
-1xy + 4xy + 2x2 + -3x2 + y2 + 3y2 = 0

Combine like terms: -1xy + 4xy = 3xy
3xy + 2x2 + -3x2 + y2 + 3y2 = 0

Combine like terms: 2x2 + -3x2 = -1x2
3xy + -1x2 + y2 + 3y2 = 0

Combine like terms: y2 + 3y2 = 4y2
3xy + -1x2 + 4y2 = 0

Solving
3xy + -1x2 + 4y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + -1y)(x + -4y) = 0


Subproblem 1
Set the factor '(-1x + -1y)' equal to zero and attempt to solve:

Simplifying
-1x + -1y = 0

Solving
-1x + -1y = 0

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

Add 'y' to each side of the equation.
-1x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-1x + 0 = 0 + y
-1x = 0 + y
Remove the zero:
-1x = y

Divide each side by '-1'.
x = -1y

Simplifying
x = -1y

Subproblem 2
Set the factor '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

Add '4y' to each side of the equation.
x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
x + 0 = 0 + 4y
x = 0 + 4y
Remove the zero:
x = 4y

Simplifying
x = 4y
Solution
x = {-1y, 4y}

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