(3x^2-4xy+7y^2)-(7x^2-6xy-3y^2)=

Solution for (3x^2-4xy+7y^2)-(7x^2-6xy-3y^2)= equation:

Simplifying
(3x2 + -4xy + 7y2) + -1(7x2 + -6xy + -3y2) = 0

Reorder the terms:
(-4xy + 3x2 + 7y2) + -1(7x2 + -6xy + -3y2) = 0

Remove parenthesis around (-4xy + 3x2 + 7y2)
-4xy + 3x2 + 7y2 + -1(7x2 + -6xy + -3y2) = 0

Reorder the terms:
-4xy + 3x2 + 7y2 + -1(-6xy + 7x2 + -3y2) = 0
-4xy + 3x2 + 7y2 + (-6xy * -1 + 7x2 * -1 + -3y2 * -1) = 0
-4xy + 3x2 + 7y2 + (6xy + -7x2 + 3y2) = 0

Reorder the terms:
-4xy + 6xy + 3x2 + -7x2 + 7y2 + 3y2 = 0

Combine like terms: -4xy + 6xy = 2xy
2xy + 3x2 + -7x2 + 7y2 + 3y2 = 0

Combine like terms: 3x2 + -7x2 = -4x2
2xy + -4x2 + 7y2 + 3y2 = 0

Combine like terms: 7y2 + 3y2 = 10y2
2xy + -4x2 + 10y2 = 0

Solving
2xy + -4x2 + 10y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xy + -2x2 + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(xy + -2x2 + 5y2)' equal to zero and attempt to solve:

Simplifying
xy + -2x2 + 5y2 = 0

Solving
xy + -2x2 + 5y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5xy + x2 + -2.5y2 = 0

Move the constant term to the right:

Add '2.5y2' to each side of the equation.
-0.5xy + x2 + -2.5y2 + 2.5y2 = 0 + 2.5y2

Combine like terms: -2.5y2 + 2.5y2 = 0.0
-0.5xy + x2 + 0.0 = 0 + 2.5y2
-0.5xy + x2 = 0 + 2.5y2
Remove the zero:
-0.5xy + x2 = 2.5y2

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.
-0.5xy + x2 + 0.25y2 = 2.5y2 + 0.25y2

Combine like terms: 2.5y2 + 0.25y2 = 2.75y2
-0.5xy + x2 + 0.25y2 = 2.75y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = 2.75y2

Calculate the square root of the right side: 1.658312395y

Break this problem into two subproblems by setting 
(x + 0.5y) equal to 1.658312395y and -1.658312395y.

Subproblem 1
x + 0.5y = 1.658312395y

Simplifying
x + 0.5y = 1.658312395y

Solving
x + 0.5y = 1.658312395y

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 = 1.658312395y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = 1.658312395y + -0.5y
x = 1.658312395y + -0.5y

Combine like terms: 1.658312395y + -0.5y = 1.158312395y
x = 1.158312395y

Simplifying
x = 1.158312395y

Subproblem 2
x + 0.5y = -1.658312395y

Simplifying
x + 0.5y = -1.658312395y

Solving
x + 0.5y = -1.658312395y

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 = -1.658312395y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = -1.658312395y + -0.5y
x = -1.658312395y + -0.5y

Combine like terms: -1.658312395y + -0.5y = -2.158312395y
x = -2.158312395y

Simplifying
x = -2.158312395y

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.158312395y, -2.158312395y}
Solution
x = {1.158312395y, -2.158312395y}