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

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

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

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

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

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) = 2(x + -3) + -1x
((1 * -1 + x * -1) + x(1 + x)) = 2(x + -3) + -1x
((-1 + -1x) + x(1 + x)) = 2(x + -3) + -1x
(-1 + -1x + (1 * x + x * x)) = 2(x + -3) + -1x
(-1 + -1x + (1x + x2)) = 2(x + -3) + -1x

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = 2(x + -3) + -1x
(-1 + x2) = 2(x + -3) + -1x

Reorder the terms:
-1 + x2 = 2(-3 + x) + -1x
-1 + x2 = (-3 * 2 + x * 2) + -1x
-1 + x2 = (-6 + 2x) + -1x

Combine like terms: 2x + -1x = 1x
-1 + x2 = -6 + 1x

Solving
-1 + x2 = -6 + 1x

Solving for variable 'x'.

Reorder the terms:
-1 + 6 + -1x + x2 = -6 + 1x + 6 + -1x

Combine like terms: -1 + 6 = 5
5 + -1x + x2 = -6 + 1x + 6 + -1x

Reorder the terms:
5 + -1x + x2 = -6 + 6 + 1x + -1x

Combine like terms: -6 + 6 = 0
5 + -1x + x2 = 0 + 1x + -1x
5 + -1x + x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
5 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -1x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -1x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x + x2 = 0 + -5
-1x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x + x2 = -5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + -1x + x2 = -4.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.