(x+y)(x+y)=

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

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

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

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

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

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

Solving
2xy + x2 + y2 = 0

Solving for variable 'x'.

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

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}