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

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

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

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

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

Multiply (3 + x) * (-5 + x)
(3(-5 + x) + x(-5 + x)) = x + 7
((-5 * 3 + x * 3) + x(-5 + x)) = x + 7
((-15 + 3x) + x(-5 + x)) = x + 7
(-15 + 3x + (-5 * x + x * x)) = x + 7
(-15 + 3x + (-5x + x2)) = x + 7

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) = x + 7

Reorder the terms:
-15 + -2x + x2 = 7 + x

Solving
-15 + -2x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-15 + -7 + -2x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -15 + -7 = -22
-22 + -2x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -2x + -1x = -3x
-22 + -3x + x2 = 7 + x + -7 + -1x

Reorder the terms:
-22 + -3x + x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-22 + -3x + x2 = 0 + x + -1x
-22 + -3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-22 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -3x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -3x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -3x + x2 = 0 + 22
-3x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-3x + x2 = 22

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 = 22 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + -3x + x2 = 24.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + -1.5 = 4.924428901

Simplifying
x + -1.5 = 4.924428901

Reorder the terms:
-1.5 + x = 4.924428901

Solving
-1.5 + x = 4.924428901

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 = 4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.924428901 + 1.5
x = 4.924428901 + 1.5

Combine like terms: 4.924428901 + 1.5 = 6.424428901
x = 6.424428901

Simplifying
x = 6.424428901

Subproblem 2
x + -1.5 = -4.924428901

Simplifying
x + -1.5 = -4.924428901

Reorder the terms:
-1.5 + x = -4.924428901

Solving
-1.5 + x = -4.924428901

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 = -4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.924428901 + 1.5
x = -4.924428901 + 1.5

Combine like terms: -4.924428901 + 1.5 = -3.424428901
x = -3.424428901

Simplifying
x = -3.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.424428901, -3.424428901}