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

Solution for (x+y)(2x+2y)=0 equation:

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

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

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

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

Combine like terms: 2xy + 2xy = 4xy
(4xy + 2x2 + 2y2) = 0

Solving
4xy + 2x2 + 2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2xy + x2 + y2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {-1y, -1y}