(x-3y)*(x-6y)=0

Solution for (x-3y)*(x-6y)=0 equation:

Simplifying
(x + -3y)(x + -6y) = 0

Multiply (x + -3y) * (x + -6y)
(x(x + -6y) + -3y * (x + -6y)) = 0
((x * x + -6y * x) + -3y * (x + -6y)) = 0

Reorder the terms:
((-6xy + x2) + -3y * (x + -6y)) = 0
((-6xy + x2) + -3y * (x + -6y)) = 0
(-6xy + x2 + (x * -3y + -6y * -3y)) = 0
(-6xy + x2 + (-3xy + 18y2)) = 0

Reorder the terms:
(-6xy + -3xy + x2 + 18y2) = 0

Combine like terms: -6xy + -3xy = -9xy
(-9xy + x2 + 18y2) = 0

Solving
-9xy + x2 + 18y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -6y)(x + -3y) = 0

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

Simplifying
x + -6y = 0

Solving
x + -6y = 0

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

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

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

Simplifying
x = 6y
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 = {6y, 3y}