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

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

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

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

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

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

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

Solving
-3 + -2x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
-3 + 2 + -2x + x2 = -2 + 2

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

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

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2x + x2 = 0 + 1

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1 + 1

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

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

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -1 = 1.414213562

Simplifying
x + -1 = 1.414213562

Reorder the terms:
-1 + x = 1.414213562

Solving
-1 + x = 1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.414213562 + 1
x = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
x = 2.414213562

Simplifying
x = 2.414213562

Subproblem 2
x + -1 = -1.414213562

Simplifying
x + -1 = -1.414213562

Reorder the terms:
-1 + x = -1.414213562

Solving
-1 + x = -1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.414213562 + 1
x = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
x = -0.414213562

Simplifying
x = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.414213562, -0.414213562}