(x-2)+3=(x+1)(x-1)+x

Solution for (x-2)+3=(x+1)(x-1)+x equation:

Simplifying
(x + -2) + 3 = (x + 1)(x + -1) + x

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

Remove parenthesis around (-2 + x)
-2 + x + 3 = (x + 1)(x + -1) + x

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

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

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

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

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

Combine like terms: 1x + -1x = 0
1 + x = (-1 + 0 + x2) + x
1 + x = (-1 + x2) + x

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

Add '-1x' to each side of the equation.
1 + x + -1x = -1 + x + -1x + x2

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

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

Solving
1 = -1 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
1 + -1x2 = -1 + x2 + -1x2

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

Add '-1' to each side of the equation.
1 + -1 + -1x2 = -1 + -1

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

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

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}