(x+20)3x=120

Solution for (x+20)3x=120 equation:

Simplifying
(x + 20) * 3x = 120

Reorder the terms:
(20 + x) * 3x = 120

Reorder the terms for easier multiplication:
3x(20 + x) = 120
(20 * 3x + x * 3x) = 120
(60x + 3x2) = 120

Solving
60x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 60x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 60x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + 20x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-40 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + 20x + x2 = 0

Solving
-40 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 20x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 20x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 20x + x2 = 0 + 40
20x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
20x + x2 = 40

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 40 + 100

Reorder the terms:
100 + 20x + x2 = 40 + 100

Combine like terms: 40 + 100 = 140
100 + 20x + x2 = 140

Factor a perfect square on the left side:
(x + 10)(x + 10) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(x + 10) equal to 11.832159566 and -11.832159566.

Subproblem 1
x + 10 = 11.832159566

Simplifying
x + 10 = 11.832159566

Reorder the terms:
10 + x = 11.832159566

Solving
10 + x = 11.832159566

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 11.832159566 + -10

Combine like terms: 10 + -10 = 0
0 + x = 11.832159566 + -10
x = 11.832159566 + -10

Combine like terms: 11.832159566 + -10 = 1.832159566
x = 1.832159566

Simplifying
x = 1.832159566

Subproblem 2
x + 10 = -11.832159566

Simplifying
x + 10 = -11.832159566

Reorder the terms:
10 + x = -11.832159566

Solving
10 + x = -11.832159566

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -11.832159566 + -10

Combine like terms: 10 + -10 = 0
0 + x = -11.832159566 + -10
x = -11.832159566 + -10

Combine like terms: -11.832159566 + -10 = -21.832159566
x = -21.832159566

Simplifying
x = -21.832159566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.832159566, -21.832159566}
Solution
x = {1.832159566, -21.832159566}