(x+3)+(x+7)(x+20)=180

Solution for (x+3)+(x+7)(x+20)=180 equation:

Simplifying
(x + 3) + (x + 7)(x + 20) = 180

Reorder the terms:
(3 + x) + (x + 7)(x + 20) = 180

Remove parenthesis around (3 + x)
3 + x + (x + 7)(x + 20) = 180

Reorder the terms:
3 + x + (7 + x)(x + 20) = 180

Reorder the terms:
3 + x + (7 + x)(20 + x) = 180

Multiply (7 + x) * (20 + x)
3 + x + (7(20 + x) + x(20 + x)) = 180
3 + x + ((20 * 7 + x * 7) + x(20 + x)) = 180
3 + x + ((140 + 7x) + x(20 + x)) = 180
3 + x + (140 + 7x + (20 * x + x * x)) = 180
3 + x + (140 + 7x + (20x + x2)) = 180

Combine like terms: 7x + 20x = 27x
3 + x + (140 + 27x + x2) = 180

Reorder the terms:
3 + 140 + x + 27x + x2 = 180

Combine like terms: 3 + 140 = 143
143 + x + 27x + x2 = 180

Combine like terms: x + 27x = 28x
143 + 28x + x2 = 180

Solving
143 + 28x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
143 + -180 + 28x + x2 = 180 + -180

Combine like terms: 143 + -180 = -37
-37 + 28x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-37 + 28x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 28x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 28x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 28x + x2 = 0 + 37
28x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
28x + x2 = 37

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 37 + 196

Reorder the terms:
196 + 28x + x2 = 37 + 196

Combine like terms: 37 + 196 = 233
196 + 28x + x2 = 233

Factor a perfect square on the left side:
(x + 14)(x + 14) = 233

Calculate the square root of the right side: 15.264337522

Break this problem into two subproblems by setting 
(x + 14) equal to 15.264337522 and -15.264337522.

Subproblem 1
x + 14 = 15.264337522

Simplifying
x + 14 = 15.264337522

Reorder the terms:
14 + x = 15.264337522

Solving
14 + x = 15.264337522

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = 15.264337522 + -14

Combine like terms: 14 + -14 = 0
0 + x = 15.264337522 + -14
x = 15.264337522 + -14

Combine like terms: 15.264337522 + -14 = 1.264337522
x = 1.264337522

Simplifying
x = 1.264337522

Subproblem 2
x + 14 = -15.264337522

Simplifying
x + 14 = -15.264337522

Reorder the terms:
14 + x = -15.264337522

Solving
14 + x = -15.264337522

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = -15.264337522 + -14

Combine like terms: 14 + -14 = 0
0 + x = -15.264337522 + -14
x = -15.264337522 + -14

Combine like terms: -15.264337522 + -14 = -29.264337522
x = -29.264337522

Simplifying
x = -29.264337522

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.264337522, -29.264337522}