2y(x+y)-3x(2x-3y)=

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Solution for 2y(x+y)-3x(2x-3y)= equation: 


Simplifying
2y(x + y) + -3x(2x + -3y) = 0
(x * 2y + y * 2y) + -3x(2x + -3y) = 0
(2xy + 2y2) + -3x(2x + -3y) = 0
2xy + 2y2 + (2x * -3x + -3y * -3x) = 0

Reorder the terms:
2xy + 2y2 + (9xy + -6x2) = 0
2xy + 2y2 + (9xy + -6x2) = 0

Reorder the terms:
2xy + 9xy + -6x2 + 2y2 = 0

Combine like terms: 2xy + 9xy = 11xy
11xy + -6x2 + 2y2 = 0

Solving
11xy + -6x2 + 2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6x + -1y)(x + -2y) = 0


Subproblem 1
Set the factor '(-6x + -1y)' equal to zero and attempt to solve:

Simplifying
-6x + -1y = 0

Solving
-6x + -1y = 0

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

Add 'y' to each side of the equation.
-6x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-6x + 0 = 0 + y
-6x = 0 + y
Remove the zero:
-6x = y

Divide each side by '-6'.
x = -0.1666666667y

Simplifying
x = -0.1666666667y

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 = {-0.1666666667y, 2y}

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