(x-5y)(3x-6y)=0

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Solution for (x-5y)(3x-6y)=0 equation: 


Simplifying
(x + -5y)(3x + -6y) = 0

Multiply (x + -5y) * (3x + -6y)
(x(3x + -6y) + -5y * (3x + -6y)) = 0
((3x * x + -6y * x) + -5y * (3x + -6y)) = 0

Reorder the terms:
((-6xy + 3x2) + -5y * (3x + -6y)) = 0
((-6xy + 3x2) + -5y * (3x + -6y)) = 0
(-6xy + 3x2 + (3x * -5y + -6y * -5y)) = 0
(-6xy + 3x2 + (-15xy + 30y2)) = 0

Reorder the terms:
(-6xy + -15xy + 3x2 + 30y2) = 0

Combine like terms: -6xy + -15xy = -21xy
(-21xy + 3x2 + 30y2) = 0

Solving
-21xy + 3x2 + 30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7xy + x2 + 10y2) = 0

Factor a trinomial.
3((x + -5y)(x + -2y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve:

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

Add '5y' to each side of the equation.
x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
x + 0 = 0 + 5y
x = 0 + 5y
Remove the zero:
x = 5y

Simplifying
x = 5y

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 = {5y, 2y}

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