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

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


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

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

Reorder the terms:
((-3xy + 2x2) + -2y * (2x + -3y)) = 0
((-3xy + 2x2) + -2y * (2x + -3y)) = 0
(-3xy + 2x2 + (2x * -2y + -3y * -2y)) = 0
(-3xy + 2x2 + (-4xy + 6y2)) = 0

Reorder the terms:
(-3xy + -4xy + 2x2 + 6y2) = 0

Combine like terms: -3xy + -4xy = -7xy
(-7xy + 2x2 + 6y2) = 0

Solving
-7xy + 2x2 + 6y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
2x + -3y = 0

Solving
2x + -3y = 0

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

Add '3y' to each side of the equation.
2x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
2x + 0 = 0 + 3y
2x = 0 + 3y
Remove the zero:
2x = 3y

Divide each side by '2'.
x = 1.5y

Simplifying
x = 1.5y
Solution
x = {2y, 1.5y}

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