2x*x+5x*y+2y*y=0

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Solution for 2x*x+5x*y+2y*y=0 equation: 


Simplifying
2x * x + 5x * y + 2y * y = 0

Multiply x * x
2x2 + 5x * y + 2y * y = 0

Multiply x * y
2x2 + 5xy + 2y * y = 0

Multiply y * y
2x2 + 5xy + 2y2 = 0

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

Solving
5xy + 2x2 + 2y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {-0.5y, -2y}

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