(x+z)(x+z)=

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

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

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

Reorder the terms:
((xz + x2) + z(x + z)) = 0
((xz + x2) + z(x + z)) = 0
(xz + x2 + (x * z + z * z)) = 0
(xz + x2 + (xz + z2)) = 0

Reorder the terms:
(xz + xz + x2 + z2) = 0

Combine like terms: xz + xz = 2xz
(2xz + x2 + z2) = 0

Solving
2xz + x2 + z2 = 0

Solving for variable 'x'.

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

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

Simplifying
x + z = 0

Solving
x + z = 0

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

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

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

Simplifying
x = -1z
Subproblem 2
Set the factor '(x + z)' equal to zero and attempt to solve:

Simplifying
x + z = 0

Solving
x + z = 0

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

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

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

Simplifying
x = -1z
Solution
x = {-1z, -1z}