2(x+1)+5=(x+3)(4-x)

Solution for 2(x+1)+5=(x+3)(4-x) equation:

Simplifying
2(x + 1) + 5 = (x + 3)(4 + -1x)

Reorder the terms:
2(1 + x) + 5 = (x + 3)(4 + -1x)
(1 * 2 + x * 2) + 5 = (x + 3)(4 + -1x)
(2 + 2x) + 5 = (x + 3)(4 + -1x)

Reorder the terms:
2 + 5 + 2x = (x + 3)(4 + -1x)

Combine like terms: 2 + 5 = 7
7 + 2x = (x + 3)(4 + -1x)

Reorder the terms:
7 + 2x = (3 + x)(4 + -1x)

Multiply (3 + x) * (4 + -1x)
7 + 2x = (3(4 + -1x) + x(4 + -1x))
7 + 2x = ((4 * 3 + -1x * 3) + x(4 + -1x))
7 + 2x = ((12 + -3x) + x(4 + -1x))
7 + 2x = (12 + -3x + (4 * x + -1x * x))
7 + 2x = (12 + -3x + (4x + -1x2))

Combine like terms: -3x + 4x = 1x
7 + 2x = (12 + 1x + -1x2)

Solving
7 + 2x = 12 + 1x + -1x2

Solving for variable 'x'.

Reorder the terms:
7 + -12 + 2x + -1x + x2 = 12 + 1x + -1x2 + -12 + -1x + x2

Combine like terms: 7 + -12 = -5
-5 + 2x + -1x + x2 = 12 + 1x + -1x2 + -12 + -1x + x2

Combine like terms: 2x + -1x = 1x
-5 + 1x + x2 = 12 + 1x + -1x2 + -12 + -1x + x2

Reorder the terms:
-5 + 1x + x2 = 12 + -12 + 1x + -1x + -1x2 + x2

Combine like terms: 12 + -12 = 0
-5 + 1x + x2 = 0 + 1x + -1x + -1x2 + x2
-5 + 1x + x2 = 1x + -1x + -1x2 + x2

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

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

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

Combine like terms: 5 + 0.25 = 5.25
0.25 + x + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + 0.5 = 2.291287847

Simplifying
x + 0.5 = 2.291287847

Reorder the terms:
0.5 + x = 2.291287847

Solving
0.5 + x = 2.291287847

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 = 2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.291287847 + -0.5
x = 2.291287847 + -0.5

Combine like terms: 2.291287847 + -0.5 = 1.791287847
x = 1.791287847

Simplifying
x = 1.791287847

Subproblem 2
x + 0.5 = -2.291287847

Simplifying
x + 0.5 = -2.291287847

Reorder the terms:
0.5 + x = -2.291287847

Solving
0.5 + x = -2.291287847

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 = -2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.291287847 + -0.5
x = -2.291287847 + -0.5

Combine like terms: -2.291287847 + -0.5 = -2.791287847
x = -2.791287847

Simplifying
x = -2.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.791287847, -2.791287847}