(x+y)(z+y)=0

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

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

Reorder the terms:
(x + y)(y + z) = 0

Multiply (x + y) * (y + z)
(x(y + z) + y(y + z)) = 0
((y * x + z * x) + y(y + z)) = 0
((xy + xz) + y(y + z)) = 0
(xy + xz + (y * y + z * y)) = 0

Reorder the terms:
(xy + xz + (yz + y2)) = 0
(xy + xz + (yz + y2)) = 0
(xy + xz + yz + y2) = 0

Solving
xy + xz + yz + y2 = 0

Solving for variable 'x'.

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

Add '-1yz' to each side of the equation.
xy + xz + yz + -1yz + y2 = 0 + -1yz

Combine like terms: yz + -1yz = 0
xy + xz + 0 + y2 = 0 + -1yz
xy + xz + y2 = 0 + -1yz
Remove the zero:
xy + xz + y2 = -1yz

Add '-1y2' to each side of the equation.
xy + xz + y2 + -1y2 = -1yz + -1y2

Combine like terms: y2 + -1y2 = 0
xy + xz + 0 = -1yz + -1y2
xy + xz = -1yz + -1y2

Reorder the terms:
xy + xz + yz + y2 = -1yz + yz + -1y2 + y2

Combine like terms: -1yz + yz = 0
xy + xz + yz + y2 = 0 + -1y2 + y2
xy + xz + yz + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
xy + xz + yz + y2 = 0

The solution to this equation could not be determined.