(x+3)(x-7)=(x-5)

Solution for (x+3)(x-7)=(x-5) equation:

Simplifying
(x + 3)(x + -7) = (x + -5)

Reorder the terms:
(3 + x)(x + -7) = (x + -5)

Reorder the terms:
(3 + x)(-7 + x) = (x + -5)

Multiply (3 + x) * (-7 + x)
(3(-7 + x) + x(-7 + x)) = (x + -5)
((-7 * 3 + x * 3) + x(-7 + x)) = (x + -5)
((-21 + 3x) + x(-7 + x)) = (x + -5)
(-21 + 3x + (-7 * x + x * x)) = (x + -5)
(-21 + 3x + (-7x + x2)) = (x + -5)

Combine like terms: 3x + -7x = -4x
(-21 + -4x + x2) = (x + -5)

Reorder the terms:
-21 + -4x + x2 = (-5 + x)

Remove parenthesis around (-5 + x)
-21 + -4x + x2 = -5 + x

Solving
-21 + -4x + x2 = -5 + x

Solving for variable 'x'.

Reorder the terms:
-21 + 5 + -4x + -1x + x2 = -5 + x + 5 + -1x

Combine like terms: -21 + 5 = -16
-16 + -4x + -1x + x2 = -5 + x + 5 + -1x

Combine like terms: -4x + -1x = -5x
-16 + -5x + x2 = -5 + x + 5 + -1x

Reorder the terms:
-16 + -5x + x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
-16 + -5x + x2 = 0 + x + -1x
-16 + -5x + x2 = x + -1x

Combine like terms: x + -1x = 0
-16 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -5x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -5x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5x + x2 = 0 + 16
-5x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-5x + x2 = 16

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 = 16 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 16 + 6.25

Combine like terms: 16 + 6.25 = 22.25
6.25 + -5x + x2 = 22.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + -2.5 = 4.716990566

Simplifying
x + -2.5 = 4.716990566

Reorder the terms:
-2.5 + x = 4.716990566

Solving
-2.5 + x = 4.716990566

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 = 4.716990566 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.716990566 + 2.5
x = 4.716990566 + 2.5

Combine like terms: 4.716990566 + 2.5 = 7.216990566
x = 7.216990566

Simplifying
x = 7.216990566

Subproblem 2
x + -2.5 = -4.716990566

Simplifying
x + -2.5 = -4.716990566

Reorder the terms:
-2.5 + x = -4.716990566

Solving
-2.5 + x = -4.716990566

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 = -4.716990566 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.716990566 + 2.5
x = -4.716990566 + 2.5

Combine like terms: -4.716990566 + 2.5 = -2.216990566
x = -2.216990566

Simplifying
x = -2.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.216990566, -2.216990566}