(x+9)(x-3)=(x+1)

Solution for (x+9)(x-3)=(x+1) equation:

Simplifying
(x + 9)(x + -3) = (x + 1)

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

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

Multiply (9 + x) * (-3 + x)
(9(-3 + x) + x(-3 + x)) = (x + 1)
((-3 * 9 + x * 9) + x(-3 + x)) = (x + 1)
((-27 + 9x) + x(-3 + x)) = (x + 1)
(-27 + 9x + (-3 * x + x * x)) = (x + 1)
(-27 + 9x + (-3x + x2)) = (x + 1)

Combine like terms: 9x + -3x = 6x
(-27 + 6x + x2) = (x + 1)

Reorder the terms:
-27 + 6x + x2 = (1 + x)

Remove parenthesis around (1 + x)
-27 + 6x + x2 = 1 + x

Solving
-27 + 6x + x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
-27 + -1 + 6x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: -27 + -1 = -28
-28 + 6x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: 6x + -1x = 5x
-28 + 5x + x2 = 1 + x + -1 + -1x

Reorder the terms:
-28 + 5x + x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-28 + 5x + x2 = 0 + x + -1x
-28 + 5x + x2 = x + -1x

Combine like terms: x + -1x = 0
-28 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 5x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 5x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 5x + x2 = 0 + 28
5x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
5x + x2 = 28

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 28 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 28 + 6.25

Combine like terms: 28 + 6.25 = 34.25
6.25 + 5x + x2 = 34.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.852349955 and -5.852349955.

Subproblem 1
x + 2.5 = 5.852349955

Simplifying
x + 2.5 = 5.852349955

Reorder the terms:
2.5 + x = 5.852349955

Solving
2.5 + x = 5.852349955

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 5.852349955 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.852349955 + -2.5
x = 5.852349955 + -2.5

Combine like terms: 5.852349955 + -2.5 = 3.352349955
x = 3.352349955

Simplifying
x = 3.352349955

Subproblem 2
x + 2.5 = -5.852349955

Simplifying
x + 2.5 = -5.852349955

Reorder the terms:
2.5 + x = -5.852349955

Solving
2.5 + x = -5.852349955

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -5.852349955 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.852349955 + -2.5
x = -5.852349955 + -2.5

Combine like terms: -5.852349955 + -2.5 = -8.352349955
x = -8.352349955

Simplifying
x = -8.352349955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.352349955, -8.352349955}