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

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

Simplifying
(x + -1)(x + -2) + 2(x + 1) = 2(x2 + 1)

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

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

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) + 2(x + 1) = 2(x2 + 1)
((-2 * -1 + x * -1) + x(-2 + x)) + 2(x + 1) = 2(x2 + 1)
((2 + -1x) + x(-2 + x)) + 2(x + 1) = 2(x2 + 1)
(2 + -1x + (-2 * x + x * x)) + 2(x + 1) = 2(x2 + 1)
(2 + -1x + (-2x + x2)) + 2(x + 1) = 2(x2 + 1)

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

Reorder the terms:
2 + -3x + x2 + 2(1 + x) = 2(x2 + 1)
2 + -3x + x2 + (1 * 2 + x * 2) = 2(x2 + 1)
2 + -3x + x2 + (2 + 2x) = 2(x2 + 1)

Reorder the terms:
2 + 2 + -3x + 2x + x2 = 2(x2 + 1)

Combine like terms: 2 + 2 = 4
4 + -3x + 2x + x2 = 2(x2 + 1)

Combine like terms: -3x + 2x = -1x
4 + -1x + x2 = 2(x2 + 1)

Reorder the terms:
4 + -1x + x2 = 2(1 + x2)
4 + -1x + x2 = (1 * 2 + x2 * 2)
4 + -1x + x2 = (2 + 2x2)

Solving
4 + -1x + x2 = 2 + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -2 + -1x + x2 + -2x2 = 2 + 2x2 + -2 + -2x2

Combine like terms: 4 + -2 = 2
2 + -1x + x2 + -2x2 = 2 + 2x2 + -2 + -2x2

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

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

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

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