(3x^2-6xy+7y^2)+(-5x^2+9xy-2y^2)=

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Solution for (3x^2-6xy+7y^2)+(-5x^2+9xy-2y^2)= equation: 


Simplifying
(3x2 + -6xy + 7y2) + (-5x2 + 9xy + -2y2) = 0

Reorder the terms:
(-6xy + 3x2 + 7y2) + (-5x2 + 9xy + -2y2) = 0

Remove parenthesis around (-6xy + 3x2 + 7y2)
-6xy + 3x2 + 7y2 + (-5x2 + 9xy + -2y2) = 0

Reorder the terms:
-6xy + 3x2 + 7y2 + (9xy + -5x2 + -2y2) = 0

Remove parenthesis around (9xy + -5x2 + -2y2)
-6xy + 3x2 + 7y2 + 9xy + -5x2 + -2y2 = 0

Reorder the terms:
-6xy + 9xy + 3x2 + -5x2 + 7y2 + -2y2 = 0

Combine like terms: -6xy + 9xy = 3xy
3xy + 3x2 + -5x2 + 7y2 + -2y2 = 0

Combine like terms: 3x2 + -5x2 = -2x2
3xy + -2x2 + 7y2 + -2y2 = 0

Combine like terms: 7y2 + -2y2 = 5y2
3xy + -2x2 + 5y2 = 0

Solving
3xy + -2x2 + 5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + -1y)(2x + -5y) = 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 '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y
Solution
x = {-1y, 2.5y}

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