(X^2+3xy-y^2)+(7x^2-5xy+12y^2)=

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Solution for (X^2+3xy-y^2)+(7x^2-5xy+12y^2)= equation: 


Simplifying
(X2 + 3xy + -1y2) + (7x2 + -5xy + 12y2) = 0

Remove parenthesis around (X2 + 3xy + -1y2)
X2 + 3xy + -1y2 + (7x2 + -5xy + 12y2) = 0

Reorder the terms:
X2 + 3xy + -1y2 + (-5xy + 7x2 + 12y2) = 0

Remove parenthesis around (-5xy + 7x2 + 12y2)
X2 + 3xy + -1y2 + -5xy + 7x2 + 12y2 = 0

Reorder the terms:
X2 + 3xy + -5xy + 7x2 + -1y2 + 12y2 = 0

Combine like terms: 3xy + -5xy = -2xy
X2 + -2xy + 7x2 + -1y2 + 12y2 = 0

Combine like terms: -1y2 + 12y2 = 11y2
X2 + -2xy + 7x2 + 11y2 = 0

Solving
X2 + -2xy + 7x2 + 11y2 = 0

Solving for variable 'X'.

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

Add '2xy' to each side of the equation.
X2 + -2xy + 7x2 + 2xy + 11y2 = 0 + 2xy

Reorder the terms:
X2 + -2xy + 2xy + 7x2 + 11y2 = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
X2 + 0 + 7x2 + 11y2 = 0 + 2xy
X2 + 7x2 + 11y2 = 0 + 2xy
Remove the zero:
X2 + 7x2 + 11y2 = 2xy

Add '-7x2' to each side of the equation.
X2 + 7x2 + -7x2 + 11y2 = 2xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
X2 + 0 + 11y2 = 2xy + -7x2
X2 + 11y2 = 2xy + -7x2

Add '-11y2' to each side of the equation.
X2 + 11y2 + -11y2 = 2xy + -7x2 + -11y2

Combine like terms: 11y2 + -11y2 = 0
X2 + 0 = 2xy + -7x2 + -11y2
X2 = 2xy + -7x2 + -11y2

Simplifying
X2 = 2xy + -7x2 + -11y2

Reorder the terms:
X2 + -2xy + 7x2 + 11y2 = 2xy + -2xy + -7x2 + 7x2 + -11y2 + 11y2

Combine like terms: 2xy + -2xy = 0
X2 + -2xy + 7x2 + 11y2 = 0 + -7x2 + 7x2 + -11y2 + 11y2
X2 + -2xy + 7x2 + 11y2 = -7x2 + 7x2 + -11y2 + 11y2

Combine like terms: -7x2 + 7x2 = 0
X2 + -2xy + 7x2 + 11y2 = 0 + -11y2 + 11y2
X2 + -2xy + 7x2 + 11y2 = -11y2 + 11y2

Combine like terms: -11y2 + 11y2 = 0
X2 + -2xy + 7x2 + 11y2 = 0

The solution to this equation could not be determined.

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