x(x-1)+2(x-1)=0

Solution for x(x-1)+2(x-1)=0 equation:

Simplifying
x(x + -1) + 2(x + -1) = 0

Reorder the terms:
x(-1 + x) + 2(x + -1) = 0
(-1 * x + x * x) + 2(x + -1) = 0
(-1x + x2) + 2(x + -1) = 0

Reorder the terms:
-1x + x2 + 2(-1 + x) = 0
-1x + x2 + (-1 * 2 + x * 2) = 0
-1x + x2 + (-2 + 2x) = 0

Reorder the terms:
-2 + -1x + 2x + x2 = 0

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

Solving
-2 + 1x + x2 = 0

Solving for variable 'x'.

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

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