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

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

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

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

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

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

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

Solving
-1 + -2x + x2 = 2

Solving for variable 'x'.

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

Combine like terms: -1 + -2 = -3
-3 + -2x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-3 + -2x + x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}