(x+20)(5x+10)=180

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Solution for (x+20)(5x+10)=180 equation: 


Simplifying
(x + 20)(5x + 10) = 180

Reorder the terms:
(20 + x)(5x + 10) = 180

Reorder the terms:
(20 + x)(10 + 5x) = 180

Multiply (20 + x) * (10 + 5x)
(20(10 + 5x) + x(10 + 5x)) = 180
((10 * 20 + 5x * 20) + x(10 + 5x)) = 180
((200 + 100x) + x(10 + 5x)) = 180
(200 + 100x + (10 * x + 5x * x)) = 180
(200 + 100x + (10x + 5x2)) = 180

Combine like terms: 100x + 10x = 110x
(200 + 110x + 5x2) = 180

Solving
200 + 110x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
200 + -180 + 110x + 5x2 = 180 + -180

Combine like terms: 200 + -180 = 20
20 + 110x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
20 + 110x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + 22x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + 22x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 22x + x2 = 0

Solving
4 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 22x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 22x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 22x + x2 = 0 + -4
22x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
22x + x2 = -4

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -4 + 121

Reorder the terms:
121 + 22x + x2 = -4 + 121

Combine like terms: -4 + 121 = 117
121 + 22x + x2 = 117

Factor a perfect square on the left side:
(x + 11)(x + 11) = 117

Calculate the square root of the right side: 10.816653826

Break this problem into two subproblems by setting 
(x + 11) equal to 10.816653826 and -10.816653826.


Subproblem 1
x + 11 = 10.816653826

Simplifying
x + 11 = 10.816653826

Reorder the terms:
11 + x = 10.816653826

Solving
11 + x = 10.816653826

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 10.816653826 + -11

Combine like terms: 11 + -11 = 0
0 + x = 10.816653826 + -11
x = 10.816653826 + -11

Combine like terms: 10.816653826 + -11 = -0.183346174
x = -0.183346174

Simplifying
x = -0.183346174


Subproblem 2
x + 11 = -10.816653826

Simplifying
x + 11 = -10.816653826

Reorder the terms:
11 + x = -10.816653826

Solving
11 + x = -10.816653826

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -10.816653826 + -11

Combine like terms: 11 + -11 = 0
0 + x = -10.816653826 + -11
x = -10.816653826 + -11

Combine like terms: -10.816653826 + -11 = -21.816653826
x = -21.816653826

Simplifying
x = -21.816653826


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.183346174, -21.816653826}
Solution
x = {-0.183346174, -21.816653826}

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