(x-2)+(x(x-2))=0

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

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

Reorder the terms:
(-2 + x) + (x(x + -2)) = 0

Remove parenthesis around (-2 + x)
-2 + x + (x(x + -2)) = 0

Reorder the terms:
-2 + x + (x(-2 + x)) = 0
-2 + x + ((-2 * x + x * x)) = 0
-2 + x + ((-2x + x2)) = 0
-2 + x + (-2x + x2) = 0

Remove parenthesis around (-2x + x2)
-2 + x + -2x + x2 = 0

Combine like terms: x + -2x = -1x
-2 + -1x + x2 = 0

Solving
-2 + -1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(2 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}