(x+y)(x-2y)=

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

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

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

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

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

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

Solving
-1xy + x2 + -2y2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y
Solution
x = {2y, -1y}