2(x+1)(x-1)=5(4-x)

Solution for 2(x+1)(x-1)=5(4-x) equation:

Simplifying
2(x + 1)(x + -1) = 5(4 + -1x)

Reorder the terms:
2(1 + x)(x + -1) = 5(4 + -1x)

Reorder the terms:
2(1 + x)(-1 + x) = 5(4 + -1x)

Multiply (1 + x) * (-1 + x)
2(1(-1 + x) + x(-1 + x)) = 5(4 + -1x)
2((-1 * 1 + x * 1) + x(-1 + x)) = 5(4 + -1x)
2((-1 + 1x) + x(-1 + x)) = 5(4 + -1x)
2(-1 + 1x + (-1 * x + x * x)) = 5(4 + -1x)
2(-1 + 1x + (-1x + x2)) = 5(4 + -1x)

Combine like terms: 1x + -1x = 0
2(-1 + 0 + x2) = 5(4 + -1x)
2(-1 + x2) = 5(4 + -1x)
(-1 * 2 + x2 * 2) = 5(4 + -1x)
(-2 + 2x2) = 5(4 + -1x)
-2 + 2x2 = (4 * 5 + -1x * 5)
-2 + 2x2 = (20 + -5x)

Solving
-2 + 2x2 = 20 + -5x

Solving for variable 'x'.

Reorder the terms:
-2 + -20 + 5x + 2x2 = 20 + -5x + -20 + 5x

Combine like terms: -2 + -20 = -22
-22 + 5x + 2x2 = 20 + -5x + -20 + 5x

Reorder the terms:
-22 + 5x + 2x2 = 20 + -20 + -5x + 5x

Combine like terms: 20 + -20 = 0
-22 + 5x + 2x2 = 0 + -5x + 5x
-22 + 5x + 2x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-22 + 5x + 2x2 = 0

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

Divide each side by '2'.
-11 + 2.5x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 2.5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 2.5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2.5x + x2 = 0 + 11
2.5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
2.5x + x2 = 11

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 11 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 11 + 1.5625

Combine like terms: 11 + 1.5625 = 12.5625
1.5625 + 2.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.54436172 and -3.54436172.

Subproblem 1
x + 1.25 = 3.54436172

Simplifying
x + 1.25 = 3.54436172

Reorder the terms:
1.25 + x = 3.54436172

Solving
1.25 + x = 3.54436172

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.54436172 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.54436172 + -1.25
x = 3.54436172 + -1.25

Combine like terms: 3.54436172 + -1.25 = 2.29436172
x = 2.29436172

Simplifying
x = 2.29436172

Subproblem 2
x + 1.25 = -3.54436172

Simplifying
x + 1.25 = -3.54436172

Reorder the terms:
1.25 + x = -3.54436172

Solving
1.25 + x = -3.54436172

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.54436172 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.54436172 + -1.25
x = -3.54436172 + -1.25

Combine like terms: -3.54436172 + -1.25 = -4.79436172
x = -4.79436172

Simplifying
x = -4.79436172

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.29436172, -4.79436172}