2x^2-9xy-5y^2=0

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Solution for 2x^2-9xy-5y^2=0 equation: 


Simplifying
2x2 + -9xy + -5y2 = 0

Reorder the terms:
-9xy + 2x2 + -5y2 = 0

Solving
-9xy + 2x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y)(2x + y) = 0


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

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

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

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

Simplifying
x = 5y

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {5y, -0.5y}

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