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

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


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

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

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

Solving for variable 'x'.

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


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

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

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

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

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {0.6y, -1y}

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