2(5x+20)2(5)x=360

Solution for 2(5x+20)2(5)x=360 equation:

Simplifying
2(5x + 20) * 2(5) * x = 360

Reorder the terms:
2(20 + 5x) * 2(5) * x = 360

Reorder the terms for easier multiplication:
2 * 2 * 5x(20 + 5x) = 360

Multiply 2 * 2
4 * 5x(20 + 5x) = 360

Multiply 4 * 5
20x(20 + 5x) = 360
(20 * 20x + 5x * 20x) = 360
(400x + 100x2) = 360

Solving
400x + 100x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 400x + 100x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 400x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-18 + 20x + 5x2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-18 + 20x + 5x2)' equal to zero and attempt to solve:

Simplifying
-18 + 20x + 5x2 = 0

Solving
-18 + 20x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-3.6 + 4x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 4x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 4x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 4x + x2 = 0 + 3.6
4x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
4x + x2 = 3.6

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 3.6 + 4

Reorder the terms:
4 + 4x + x2 = 3.6 + 4

Combine like terms: 3.6 + 4 = 7.6
4 + 4x + x2 = 7.6

Factor a perfect square on the left side:
(x + 2)(x + 2) = 7.6

Calculate the square root of the right side: 2.75680975

Break this problem into two subproblems by setting 
(x + 2) equal to 2.75680975 and -2.75680975.

Subproblem 1
x + 2 = 2.75680975

Simplifying
x + 2 = 2.75680975

Reorder the terms:
2 + x = 2.75680975

Solving
2 + x = 2.75680975

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.75680975 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.75680975 + -2
x = 2.75680975 + -2

Combine like terms: 2.75680975 + -2 = 0.75680975
x = 0.75680975

Simplifying
x = 0.75680975

Subproblem 2
x + 2 = -2.75680975

Simplifying
x + 2 = -2.75680975

Reorder the terms:
2 + x = -2.75680975

Solving
2 + x = -2.75680975

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.75680975 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.75680975 + -2
x = -2.75680975 + -2

Combine like terms: -2.75680975 + -2 = -4.75680975
x = -4.75680975

Simplifying
x = -4.75680975

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.75680975, -4.75680975}
Solution
x = {0.75680975, -4.75680975}