X^2-xy-2y^2=(x+y)(x-2y)

Solution for X^2-xy-2y^2=(x+y)(x-2y) equation:

Simplifying
X2 + -1xy + -2y2 = (x + y)(x + -2y)

Multiply (x + y) * (x + -2y)
X2 + -1xy + -2y2 = (x(x + -2y) + y(x + -2y))
X2 + -1xy + -2y2 = ((x * x + -2y * x) + y(x + -2y))

Reorder the terms:
X2 + -1xy + -2y2 = ((-2xy + x2) + y(x + -2y))
X2 + -1xy + -2y2 = ((-2xy + x2) + y(x + -2y))
X2 + -1xy + -2y2 = (-2xy + x2 + (x * y + -2y * y))
X2 + -1xy + -2y2 = (-2xy + x2 + (xy + -2y2))

Reorder the terms:
X2 + -1xy + -2y2 = (-2xy + xy + x2 + -2y2)

Combine like terms: -2xy + xy = -1xy
X2 + -1xy + -2y2 = (-1xy + x2 + -2y2)

Add 'xy' to each side of the equation.
X2 + -1xy + xy + -2y2 = -1xy + x2 + xy + -2y2

Combine like terms: -1xy + xy = 0
X2 + 0 + -2y2 = -1xy + x2 + xy + -2y2
X2 + -2y2 = -1xy + x2 + xy + -2y2

Reorder the terms:
X2 + -2y2 = -1xy + xy + x2 + -2y2

Combine like terms: -1xy + xy = 0
X2 + -2y2 = 0 + x2 + -2y2
X2 + -2y2 = x2 + -2y2

Add '2y2' to each side of the equation.
X2 + -2y2 + 2y2 = x2 + -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
X2 + 0 = x2 + -2y2 + 2y2
X2 = x2 + -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
X2 = x2 + 0
X2 = x2

Solving
X2 = x2

Solving for variable 'X'.

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

Simplifying
X2 = x2

Take the square root of each side:
X = {-1x, x}