0=6x^2+3y^2-9xy

Solution for 0=6x^2+3y^2-9xy equation:

Simplifying
0 = 6x2 + 3y2 + -9xy

Reorder the terms:
0 = -9xy + 6x2 + 3y2

Solving
0 = -9xy + 6x2 + 3y2

Solving for variable 'x'.
Remove the zero:
9xy + -6x2 + -3y2 = -9xy + 6x2 + 3y2 + 9xy + -6x2 + -3y2

Reorder the terms:
9xy + -6x2 + -3y2 = -9xy + 9xy + 6x2 + -6x2 + 3y2 + -3y2

Combine like terms: -9xy + 9xy = 0
9xy + -6x2 + -3y2 = 0 + 6x2 + -6x2 + 3y2 + -3y2
9xy + -6x2 + -3y2 = 6x2 + -6x2 + 3y2 + -3y2

Combine like terms: 6x2 + -6x2 = 0
9xy + -6x2 + -3y2 = 0 + 3y2 + -3y2
9xy + -6x2 + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
9xy + -6x2 + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3xy + -2x2 + -1y2) = 0

Factor a trinomial.
3((-2x + y)(x + -1y)) = 0

Ignore the factor 3.
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 + -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 = {0.5y, y}