x^2-xy=6y^2

Solution for x^2-xy=6y^2 equation:

Simplifying
x2 + -1xy = 6y2

Reorder the terms:
-1xy + x2 = 6y2

Solving
-1xy + x2 = 6y2

Solving for variable 'x'.

Combine like terms: 6y2 + -6y2 = 0
-1xy + x2 + -6y2 = 0

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}