5y^2-2xy-3x^2=0

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Solution for 5y^2-2xy-3x^2=0 equation: 


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

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

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

Solving for variable 'x'.

Factor a trinomial.
(-3x + -5y)(x + -1y) = 0


Subproblem 1
Set the factor '(-3x + -5y)' equal to zero and attempt to solve:

Simplifying
-3x + -5y = 0

Solving
-3x + -5y = 0

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

Add '5y' to each side of the equation.
-3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-3x + 0 = 0 + 5y
-3x = 0 + 5y
Remove the zero:
-3x = 5y

Divide each side by '-3'.
x = -1.666666667y

Simplifying
x = -1.666666667y

Subproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y
Solution
x = {-1.666666667y, y}

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