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

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

Simplifying
3x + 20 + (3x + -20) * 3x + (x + 20) = 180

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

Reorder the terms for easier multiplication:
3x + 20 + 3x(-20 + 3x) + (x + 20) = 180
3x + 20 + (-20 * 3x + 3x * 3x) + (x + 20) = 180
3x + 20 + (-60x + 9x2) + (x + 20) = 180

Reorder the terms:
3x + 20 + -60x + 9x2 + (20 + x) = 180

Remove parenthesis around (20 + x)
3x + 20 + -60x + 9x2 + 20 + x = 180

Reorder the terms:
20 + 20 + 3x + -60x + x + 9x2 = 180

Combine like terms: 20 + 20 = 40
40 + 3x + -60x + x + 9x2 = 180

Combine like terms: 3x + -60x = -57x
40 + -57x + x + 9x2 = 180

Combine like terms: -57x + x = -56x
40 + -56x + 9x2 = 180

Solving
40 + -56x + 9x2 = 180

Solving for variable 'x'.

Reorder the terms:
40 + -180 + -56x + 9x2 = 180 + -180

Combine like terms: 40 + -180 = -140
-140 + -56x + 9x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-140 + -56x + 9x2 = 0

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

Divide each side by '9'.
-15.55555556 + -6.222222222x + x2 = 0

Move the constant term to the right:

Add '15.55555556' to each side of the equation.
-15.55555556 + -6.222222222x + 15.55555556 + x2 = 0 + 15.55555556

Reorder the terms:
-15.55555556 + 15.55555556 + -6.222222222x + x2 = 0 + 15.55555556

Combine like terms: -15.55555556 + 15.55555556 = 0.00000000
0.00000000 + -6.222222222x + x2 = 0 + 15.55555556
-6.222222222x + x2 = 0 + 15.55555556

Combine like terms: 0 + 15.55555556 = 15.55555556
-6.222222222x + x2 = 15.55555556

The x term is -6.222222222x.  Take half its coefficient (-3.111111111).
Square it (9.679012345) and add it to both sides.

Add '9.679012345' to each side of the equation.
-6.222222222x + 9.679012345 + x2 = 15.55555556 + 9.679012345

Reorder the terms:
9.679012345 + -6.222222222x + x2 = 15.55555556 + 9.679012345

Combine like terms: 15.55555556 + 9.679012345 = 25.234567905
9.679012345 + -6.222222222x + x2 = 25.234567905

Factor a perfect square on the left side:
(x + -3.111111111)(x + -3.111111111) = 25.234567905

Calculate the square root of the right side: 5.023402025

Break this problem into two subproblems by setting 
(x + -3.111111111) equal to 5.023402025 and -5.023402025.

Subproblem 1
x + -3.111111111 = 5.023402025

Simplifying
x + -3.111111111 = 5.023402025

Reorder the terms:
-3.111111111 + x = 5.023402025

Solving
-3.111111111 + x = 5.023402025

Solving for variable 'x'.

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

Add '3.111111111' to each side of the equation.
-3.111111111 + 3.111111111 + x = 5.023402025 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + x = 5.023402025 + 3.111111111
x = 5.023402025 + 3.111111111

Combine like terms: 5.023402025 + 3.111111111 = 8.134513136
x = 8.134513136

Simplifying
x = 8.134513136

Subproblem 2
x + -3.111111111 = -5.023402025

Simplifying
x + -3.111111111 = -5.023402025

Reorder the terms:
-3.111111111 + x = -5.023402025

Solving
-3.111111111 + x = -5.023402025

Solving for variable 'x'.

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

Add '3.111111111' to each side of the equation.
-3.111111111 + 3.111111111 + x = -5.023402025 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + x = -5.023402025 + 3.111111111
x = -5.023402025 + 3.111111111

Combine like terms: -5.023402025 + 3.111111111 = -1.912290914
x = -1.912290914

Simplifying
x = -1.912290914

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.134513136, -1.912290914}