(x+4)(x-20)+13=x

Solution for (x+4)(x-20)+13=x equation:

Simplifying
(x + 4)(x + -20) + 13 = x

Reorder the terms:
(4 + x)(x + -20) + 13 = x

Reorder the terms:
(4 + x)(-20 + x) + 13 = x

Multiply (4 + x) * (-20 + x)
(4(-20 + x) + x(-20 + x)) + 13 = x
((-20 * 4 + x * 4) + x(-20 + x)) + 13 = x
((-80 + 4x) + x(-20 + x)) + 13 = x
(-80 + 4x + (-20 * x + x * x)) + 13 = x
(-80 + 4x + (-20x + x2)) + 13 = x

Combine like terms: 4x + -20x = -16x
(-80 + -16x + x2) + 13 = x

Reorder the terms:
-80 + 13 + -16x + x2 = x

Combine like terms: -80 + 13 = -67
-67 + -16x + x2 = x

Solving
-67 + -16x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-67 + -16x + -1x + x2 = x + -1x

Combine like terms: -16x + -1x = -17x
-67 + -17x + x2 = x + -1x

Combine like terms: x + -1x = 0
-67 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + -17x + 67 + x2 = 0 + 67

Reorder the terms:
-67 + 67 + -17x + x2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -17x + x2 = 0 + 67
-17x + x2 = 0 + 67

Combine like terms: 0 + 67 = 67
-17x + x2 = 67

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 67 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 67 + 72.25

Combine like terms: 67 + 72.25 = 139.25
72.25 + -17x + x2 = 139.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 139.25

Calculate the square root of the right side: 11.800423721

Break this problem into two subproblems by setting 
(x + -8.5) equal to 11.800423721 and -11.800423721.

Subproblem 1
x + -8.5 = 11.800423721

Simplifying
x + -8.5 = 11.800423721

Reorder the terms:
-8.5 + x = 11.800423721

Solving
-8.5 + x = 11.800423721

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 11.800423721 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 11.800423721 + 8.5
x = 11.800423721 + 8.5

Combine like terms: 11.800423721 + 8.5 = 20.300423721
x = 20.300423721

Simplifying
x = 20.300423721

Subproblem 2
x + -8.5 = -11.800423721

Simplifying
x + -8.5 = -11.800423721

Reorder the terms:
-8.5 + x = -11.800423721

Solving
-8.5 + x = -11.800423721

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -11.800423721 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -11.800423721 + 8.5
x = -11.800423721 + 8.5

Combine like terms: -11.800423721 + 8.5 = -3.300423721
x = -3.300423721

Simplifying
x = -3.300423721

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.300423721, -3.300423721}