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

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

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

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

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

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

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

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

Remove parenthesis around (3 + x)
-1 + x2 = 3 + x

Solving
-1 + x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -3 + -1x + x2 = 3 + x + -3 + -1x

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

Reorder the terms:
-4 + -1x + x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-4 + -1x + x2 = 0 + x + -1x
-4 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -1x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x + x2 = 0 + 4
-1x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x + x2 = 4

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 = 4 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -1x + x2 = 4.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + -0.5 = 2.061552813

Simplifying
x + -0.5 = 2.061552813

Reorder the terms:
-0.5 + x = 2.061552813

Solving
-0.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.061552813 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.061552813 + 0.5
x = 2.061552813 + 0.5

Combine like terms: 2.061552813 + 0.5 = 2.561552813
x = 2.561552813

Simplifying
x = 2.561552813

Subproblem 2
x + -0.5 = -2.061552813

Simplifying
x + -0.5 = -2.061552813

Reorder the terms:
-0.5 + x = -2.061552813

Solving
-0.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.061552813 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.061552813 + 0.5
x = -2.061552813 + 0.5

Combine like terms: -2.061552813 + 0.5 = -1.561552813
x = -1.561552813

Simplifying
x = -1.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.561552813, -1.561552813}