(2x+10)(x+5)=180

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Solution for (2x+10)(x+5)=180 equation: 


Simplifying
(2x + 10)(x + 5) = 180

Reorder the terms:
(10 + 2x)(x + 5) = 180

Reorder the terms:
(10 + 2x)(5 + x) = 180

Multiply (10 + 2x) * (5 + x)
(10(5 + x) + 2x * (5 + x)) = 180
((5 * 10 + x * 10) + 2x * (5 + x)) = 180
((50 + 10x) + 2x * (5 + x)) = 180
(50 + 10x + (5 * 2x + x * 2x)) = 180
(50 + 10x + (10x + 2x2)) = 180

Combine like terms: 10x + 10x = 20x
(50 + 20x + 2x2) = 180

Solving
50 + 20x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
50 + -180 + 20x + 2x2 = 180 + -180

Combine like terms: 50 + -180 = -130
-130 + 20x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-130 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-65 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-65 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-65 + 10x + x2 = 0

Solving
-65 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + 10x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + 10x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 10x + x2 = 0 + 65
10x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
10x + x2 = 65

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 65 + 25

Reorder the terms:
25 + 10x + x2 = 65 + 25

Combine like terms: 65 + 25 = 90
25 + 10x + x2 = 90

Factor a perfect square on the left side:
(x + 5)(x + 5) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(x + 5) equal to 9.486832981 and -9.486832981.


Subproblem 1
x + 5 = 9.486832981

Simplifying
x + 5 = 9.486832981

Reorder the terms:
5 + x = 9.486832981

Solving
5 + x = 9.486832981

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 9.486832981 + -5

Combine like terms: 5 + -5 = 0
0 + x = 9.486832981 + -5
x = 9.486832981 + -5

Combine like terms: 9.486832981 + -5 = 4.486832981
x = 4.486832981

Simplifying
x = 4.486832981


Subproblem 2
x + 5 = -9.486832981

Simplifying
x + 5 = -9.486832981

Reorder the terms:
5 + x = -9.486832981

Solving
5 + x = -9.486832981

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -9.486832981 + -5

Combine like terms: 5 + -5 = 0
0 + x = -9.486832981 + -5
x = -9.486832981 + -5

Combine like terms: -9.486832981 + -5 = -14.486832981
x = -14.486832981

Simplifying
x = -14.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.486832981, -14.486832981}
Solution
x = {4.486832981, -14.486832981}

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