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

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


Simplifying
(x + -2y)(y + -3x) = 0

Reorder the terms:
(x + -2y)(-3x + y) = 0

Multiply (x + -2y) * (-3x + y)
(x(-3x + y) + -2y * (-3x + y)) = 0
((-3x * x + y * x) + -2y * (-3x + y)) = 0

Reorder the terms:
((xy + -3x2) + -2y * (-3x + y)) = 0
((xy + -3x2) + -2y * (-3x + y)) = 0
(xy + -3x2 + (-3x * -2y + y * -2y)) = 0
(xy + -3x2 + (6xy + -2y2)) = 0

Reorder the terms:
(xy + 6xy + -3x2 + -2y2) = 0

Combine like terms: xy + 6xy = 7xy
(7xy + -3x2 + -2y2) = 0

Solving
7xy + -3x2 + -2y2 = 0

Solving for variable 'x'.

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


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

Simplifying
-3x + y = 0

Solving
-3x + y = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y

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 = {0.3333333333y, 2y}

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