x(x+z)=

Solution for x(x+z)= equation:

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

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

Solving
xz + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(z + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(z + x)' equal to zero and attempt to solve:

Simplifying
z + x = 0

Reorder the terms:
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 = {0, -1z}