(x+9)(x-5)=(x+1)

Solution for (x+9)(x-5)=(x+1) equation:

Simplifying
(x + 9)(x + -5) = (x + 1)

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

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

Multiply (9 + x) * (-5 + x)
(9(-5 + x) + x(-5 + x)) = (x + 1)
((-5 * 9 + x * 9) + x(-5 + x)) = (x + 1)
((-45 + 9x) + x(-5 + x)) = (x + 1)
(-45 + 9x + (-5 * x + x * x)) = (x + 1)
(-45 + 9x + (-5x + x2)) = (x + 1)

Combine like terms: 9x + -5x = 4x
(-45 + 4x + x2) = (x + 1)

Reorder the terms:
-45 + 4x + x2 = (1 + x)

Remove parenthesis around (1 + x)
-45 + 4x + x2 = 1 + x

Solving
-45 + 4x + x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
-45 + -1 + 4x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: -45 + -1 = -46
-46 + 4x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: 4x + -1x = 3x
-46 + 3x + x2 = 1 + x + -1 + -1x

Reorder the terms:
-46 + 3x + x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-46 + 3x + x2 = 0 + x + -1x
-46 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-46 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 3x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 3x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 3x + x2 = 0 + 46
3x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
3x + x2 = 46

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 46 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 46 + 2.25

Combine like terms: 46 + 2.25 = 48.25
2.25 + 3x + x2 = 48.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.946221995 and -6.946221995.

Subproblem 1
x + 1.5 = 6.946221995

Simplifying
x + 1.5 = 6.946221995

Reorder the terms:
1.5 + x = 6.946221995

Solving
1.5 + x = 6.946221995

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 6.946221995 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6.946221995 + -1.5
x = 6.946221995 + -1.5

Combine like terms: 6.946221995 + -1.5 = 5.446221995
x = 5.446221995

Simplifying
x = 5.446221995

Subproblem 2
x + 1.5 = -6.946221995

Simplifying
x + 1.5 = -6.946221995

Reorder the terms:
1.5 + x = -6.946221995

Solving
1.5 + x = -6.946221995

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -6.946221995 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6.946221995 + -1.5
x = -6.946221995 + -1.5

Combine like terms: -6.946221995 + -1.5 = -8.446221995
x = -8.446221995

Simplifying
x = -8.446221995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.446221995, -8.446221995}