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

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

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

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

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

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

Combine like terms: 9x + -1x = 8x
(-9 + 8x + x2) = (x + 3)

Reorder the terms:
-9 + 8x + x2 = (3 + x)

Remove parenthesis around (3 + x)
-9 + 8x + x2 = 3 + x

Solving
-9 + 8x + x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-9 + -3 + 8x + -1x + x2 = 3 + x + -3 + -1x

Combine like terms: -9 + -3 = -12
-12 + 8x + -1x + x2 = 3 + x + -3 + -1x

Combine like terms: 8x + -1x = 7x
-12 + 7x + x2 = 3 + x + -3 + -1x

Reorder the terms:
-12 + 7x + x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-12 + 7x + x2 = 0 + x + -1x
-12 + 7x + x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 7x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 7x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7x + x2 = 0 + 12
7x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
7x + x2 = 12

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 12 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + 7x + x2 = 24.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + 3.5 = 4.924428901

Simplifying
x + 3.5 = 4.924428901

Reorder the terms:
3.5 + x = 4.924428901

Solving
3.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.924428901 + -3.5
x = 4.924428901 + -3.5

Combine like terms: 4.924428901 + -3.5 = 1.424428901
x = 1.424428901

Simplifying
x = 1.424428901

Subproblem 2
x + 3.5 = -4.924428901

Simplifying
x + 3.5 = -4.924428901

Reorder the terms:
3.5 + x = -4.924428901

Solving
3.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.924428901 + -3.5
x = -4.924428901 + -3.5

Combine like terms: -4.924428901 + -3.5 = -8.424428901
x = -8.424428901

Simplifying
x = -8.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.424428901, -8.424428901}