2(x+1)(x-3)=5

Solution for 2(x+1)(x-3)=5 equation:

Simplifying
2(x + 1)(x + -3) = 5

Reorder the terms:
2(1 + x)(x + -3) = 5

Reorder the terms:
2(1 + x)(-3 + x) = 5

Multiply (1 + x) * (-3 + x)
2(1(-3 + x) + x(-3 + x)) = 5
2((-3 * 1 + x * 1) + x(-3 + x)) = 5
2((-3 + 1x) + x(-3 + x)) = 5
2(-3 + 1x + (-3 * x + x * x)) = 5
2(-3 + 1x + (-3x + x2)) = 5

Combine like terms: 1x + -3x = -2x
2(-3 + -2x + x2) = 5
(-3 * 2 + -2x * 2 + x2 * 2) = 5
(-6 + -4x + 2x2) = 5

Solving
-6 + -4x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-6 + -5 + -4x + 2x2 = 5 + -5

Combine like terms: -6 + -5 = -11
-11 + -4x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-11 + -4x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-5.5 + -2x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -2x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -2x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -2x + x2 = 0 + 5.5
-2x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-2x + x2 = 5.5

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 = 5.5 + 1

Reorder the terms:
1 + -2x + x2 = 5.5 + 1

Combine like terms: 5.5 + 1 = 6.5
1 + -2x + x2 = 6.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + -1) equal to 2.549509757 and -2.549509757.

Subproblem 1
x + -1 = 2.549509757

Simplifying
x + -1 = 2.549509757

Reorder the terms:
-1 + x = 2.549509757

Solving
-1 + x = 2.549509757

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 = 2.549509757 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.549509757 + 1
x = 2.549509757 + 1

Combine like terms: 2.549509757 + 1 = 3.549509757
x = 3.549509757

Simplifying
x = 3.549509757

Subproblem 2
x + -1 = -2.549509757

Simplifying
x + -1 = -2.549509757

Reorder the terms:
-1 + x = -2.549509757

Solving
-1 + x = -2.549509757

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 = -2.549509757 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.549509757 + 1
x = -2.549509757 + 1

Combine like terms: -2.549509757 + 1 = -1.549509757
x = -1.549509757

Simplifying
x = -1.549509757

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.549509757, -1.549509757}