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

Solution for (x-3y)(x-2y)=0 equation:

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

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

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

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

Combine like terms: -2xy + -3xy = -5xy
(-5xy + x2 + 6y2) = 0

Solving
-5xy + x2 + 6y2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
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 = {3y, 2y}