2x^2-9xy+4y^2=0

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Solution for 2x^2-9xy+4y^2=0 equation: 


Simplifying
2x2 + -9xy + 4y2 = 0

Reorder the terms:
-9xy + 2x2 + 4y2 = 0

Solving
-9xy + 2x2 + 4y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -4y)(2x + -1y) = 0


Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

Add '4y' to each side of the equation.
x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
x + 0 = 0 + 4y
x = 0 + 4y
Remove the zero:
x = 4y

Simplifying
x = 4y

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

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

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

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

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

Simplifying
x = 0.5y
Solution
x = {4y, 0.5y}

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