(x+10)(x+20)=180

Solution for (x+10)(x+20)=180 equation:

Simplifying
(x + 10)(x + 20) = 180

Reorder the terms:
(10 + x)(x + 20) = 180

Reorder the terms:
(10 + x)(20 + x) = 180

Multiply (10 + x) * (20 + x)
(10(20 + x) + x(20 + x)) = 180
((20 * 10 + x * 10) + x(20 + x)) = 180
((200 + 10x) + x(20 + x)) = 180
(200 + 10x + (20 * x + x * x)) = 180
(200 + 10x + (20x + x2)) = 180

Combine like terms: 10x + 20x = 30x
(200 + 30x + x2) = 180

Solving
200 + 30x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
200 + -180 + 30x + x2 = 180 + -180

Combine like terms: 200 + -180 = 20
20 + 30x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
20 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 30x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 30x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 30x + x2 = 0 + -20
30x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
30x + x2 = -20

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -20 + 225

Reorder the terms:
225 + 30x + x2 = -20 + 225

Combine like terms: -20 + 225 = 205
225 + 30x + x2 = 205

Factor a perfect square on the left side:
(x + 15)(x + 15) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(x + 15) equal to 14.317821063 and -14.317821063.

Subproblem 1
x + 15 = 14.317821063

Simplifying
x + 15 = 14.317821063

Reorder the terms:
15 + x = 14.317821063

Solving
15 + x = 14.317821063

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 14.317821063 + -15

Combine like terms: 15 + -15 = 0
0 + x = 14.317821063 + -15
x = 14.317821063 + -15

Combine like terms: 14.317821063 + -15 = -0.682178937
x = -0.682178937

Simplifying
x = -0.682178937

Subproblem 2
x + 15 = -14.317821063

Simplifying
x + 15 = -14.317821063

Reorder the terms:
15 + x = -14.317821063

Solving
15 + x = -14.317821063

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -14.317821063 + -15

Combine like terms: 15 + -15 = 0
0 + x = -14.317821063 + -15
x = -14.317821063 + -15

Combine like terms: -14.317821063 + -15 = -29.317821063
x = -29.317821063

Simplifying
x = -29.317821063

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.682178937, -29.317821063}