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

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

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

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

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

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

Solving
2 + 1x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(1 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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