=(x+y)(x-y)+(2x-y)(3x+y)

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

Simplifying
0 = (x + y)(x + -1y) + (2x + -1y)(3x + y)

Multiply (x + y) * (x + -1y)
0 = (x(x + -1y) + y(x + -1y)) + (2x + -1y)(3x + y)
0 = ((x * x + -1y * x) + y(x + -1y)) + (2x + -1y)(3x + y)

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

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

Combine like terms: -1xy + xy = 0
0 = (0 + x2 + -1y2) + (2x + -1y)(3x + y)
0 = (x2 + -1y2) + (2x + -1y)(3x + y)

Multiply (2x + -1y) * (3x + y)
0 = x2 + -1y2 + (2x * (3x + y) + -1y * (3x + y))
0 = x2 + -1y2 + ((3x * 2x + y * 2x) + -1y * (3x + y))

Reorder the terms:
0 = x2 + -1y2 + ((2xy + 6x2) + -1y * (3x + y))
0 = x2 + -1y2 + ((2xy + 6x2) + -1y * (3x + y))
0 = x2 + -1y2 + (2xy + 6x2 + (3x * -1y + y * -1y))
0 = x2 + -1y2 + (2xy + 6x2 + (-3xy + -1y2))

Reorder the terms:
0 = x2 + -1y2 + (2xy + -3xy + 6x2 + -1y2)

Combine like terms: 2xy + -3xy = -1xy
0 = x2 + -1y2 + (-1xy + 6x2 + -1y2)

Reorder the terms:
0 = -1xy + x2 + 6x2 + -1y2 + -1y2

Combine like terms: x2 + 6x2 = 7x2
0 = -1xy + 7x2 + -1y2 + -1y2

Combine like terms: -1y2 + -1y2 = -2y2
0 = -1xy + 7x2 + -2y2

Solving
0 = -1xy + 7x2 + -2y2

Solving for variable 'x'.
Remove the zero:
xy + -7x2 + 2y2 = -1xy + 7x2 + -2y2 + xy + -7x2 + 2y2

Reorder the terms:
xy + -7x2 + 2y2 = -1xy + xy + 7x2 + -7x2 + -2y2 + 2y2

Combine like terms: -1xy + xy = 0
xy + -7x2 + 2y2 = 0 + 7x2 + -7x2 + -2y2 + 2y2
xy + -7x2 + 2y2 = 7x2 + -7x2 + -2y2 + 2y2

Combine like terms: 7x2 + -7x2 = 0
xy + -7x2 + 2y2 = 0 + -2y2 + 2y2
xy + -7x2 + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
xy + -7x2 + 2y2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.1428571429xy + x2 + -0.2857142857y2 = 0

Move the constant term to the right:

Add '0.2857142857y2' to each side of the equation.
-0.1428571429xy + x2 + -0.2857142857y2 + 0.2857142857y2 = 0 + 0.2857142857y2

Combine like terms: -0.2857142857y2 + 0.2857142857y2 = 0.0000000000
-0.1428571429xy + x2 + 0.0000000000 = 0 + 0.2857142857y2
-0.1428571429xy + x2 = 0 + 0.2857142857y2
Remove the zero:
-0.1428571429xy + x2 = 0.2857142857y2

The x term is xy.  Take half its coefficient (0.5y).
Square it (0.25y2) and add it to both sides.

Add '0.25y2' to each side of the equation.
-0.1428571429xy + x2 + 0.25y2 = 0.2857142857y2 + 0.25y2

Combine like terms: 0.2857142857y2 + 0.25y2 = 0.5357142857y2
-0.1428571429xy + x2 + 0.25y2 = 0.5357142857y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = 0.5357142857y2

Calculate the square root of the right side: 0.731925055y

Break this problem into two subproblems by setting 
(x + 0.5y) equal to 0.731925055y and -0.731925055y.

Subproblem 1
x + 0.5y = 0.731925055y

Simplifying
x + 0.5y = 0.731925055y

Solving
x + 0.5y = 0.731925055y

Solving for variable 'x'.

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

Add '-0.5y' to each side of the equation.
x + 0.5y + -0.5y = 0.731925055y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = 0.731925055y + -0.5y
x = 0.731925055y + -0.5y

Combine like terms: 0.731925055y + -0.5y = 0.231925055y
x = 0.231925055y

Simplifying
x = 0.231925055y

Subproblem 2
x + 0.5y = -0.731925055y

Simplifying
x + 0.5y = -0.731925055y

Solving
x + 0.5y = -0.731925055y

Solving for variable 'x'.

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

Add '-0.5y' to each side of the equation.
x + 0.5y + -0.5y = -0.731925055y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = -0.731925055y + -0.5y
x = -0.731925055y + -0.5y

Combine like terms: -0.731925055y + -0.5y = -1.231925055y
x = -1.231925055y

Simplifying
x = -1.231925055y

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.231925055y, -1.231925055y}