y^2-2yx-3x^2=0

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Solution for y^2-2yx-3x^2=0 equation: 


Simplifying
y2 + -2yx + -3x2 = 0

Reorder the terms:
-2xy + -3x2 + y2 = 0

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

Solving for variable 'x'.

Factor a trinomial.
(-1x + -1y)(3x + -1y) = 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 '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {-1y, 0.3333333333y}

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