(6x^2+4y^2)+(5x^2-3y^2)=x^2+y^2

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Solution for (6x^2+4y^2)+(5x^2-3y^2)=x^2+y^2 equation: 


Simplifying
(6x2 + 4y2) + (5x2 + -3y2) = x2 + y2

Remove parenthesis around (6x2 + 4y2)
6x2 + 4y2 + (5x2 + -3y2) = x2 + y2

Remove parenthesis around (5x2 + -3y2)
6x2 + 4y2 + 5x2 + -3y2 = x2 + y2

Reorder the terms:
6x2 + 5x2 + 4y2 + -3y2 = x2 + y2

Combine like terms: 6x2 + 5x2 = 11x2
11x2 + 4y2 + -3y2 = x2 + y2

Combine like terms: 4y2 + -3y2 = 1y2
11x2 + 1y2 = x2 + y2

Solving
11x2 + 1y2 = x2 + y2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
11x2 + -1x2 + 1y2 = x2 + -1x2 + y2

Combine like terms: 11x2 + -1x2 = 10x2
10x2 + 1y2 = x2 + -1x2 + y2

Combine like terms: x2 + -1x2 = 0
10x2 + 1y2 = 0 + y2
10x2 + 1y2 = y2

Add '-1y2' to each side of the equation.
10x2 + 1y2 + -1y2 = y2 + -1y2

Combine like terms: 1y2 + -1y2 = 0
10x2 + 0 = y2 + -1y2
10x2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
10x2 = 0

Divide each side by '10'.
x2 = 0.0

Simplifying
x2 = 0.0

Take the square root of each side:
x = {0.0}

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