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

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


Simplifying
6xy + -1x2 + -9y2 = 0

Solving
6xy + -1x2 + -9y2 = 0

Solving for variable 'x'.

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


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

Simplifying
-1x + 3y = 0

Solving
-1x + 3y = 0

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

Add '-3y' to each side of the equation.
-1x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-1x + 0 = 0 + -3y
-1x = 0 + -3y
Remove the zero:
-1x = -3y

Divide each side by '-1'.
x = 3y

Simplifying
x = 3y

Subproblem 2
Set the factor '(x + -3y)' equal to zero and attempt to solve:

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y
Solution
x = {3y, 3y}

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