60(x+20)3x=180

Solution for 60(x+20)3x=180 equation:

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

Reorder the terms:
60(20 + x) * 3x = 180

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

Multiply 60 * 3
180x(20 + x) = 180
(20 * 180x + x * 180x) = 180
(3600x + 180x2) = 180

Solving
3600x + 180x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 3600x + 180x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 3600x + 180x2 = 0

Factor out the Greatest Common Factor (GCF), '180'.
180(-1 + 20x + x2) = 0

Ignore the factor 180.
Subproblem 1
Set the factor '(-1 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + 20x + x2 = 0

Solving
-1 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 20x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 20x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 20x + x2 = 0 + 1
20x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
20x + x2 = 1

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 = 1 + 100

Reorder the terms:
100 + 20x + x2 = 1 + 100

Combine like terms: 1 + 100 = 101
100 + 20x + x2 = 101

Factor a perfect square on the left side:
(x + 10)(x + 10) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + 10) equal to 10.049875621 and -10.049875621.

Subproblem 1
x + 10 = 10.049875621

Simplifying
x + 10 = 10.049875621

Reorder the terms:
10 + x = 10.049875621

Solving
10 + x = 10.049875621

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 = 10.049875621 + -10

Combine like terms: 10 + -10 = 0
0 + x = 10.049875621 + -10
x = 10.049875621 + -10

Combine like terms: 10.049875621 + -10 = 0.049875621
x = 0.049875621

Simplifying
x = 0.049875621

Subproblem 2
x + 10 = -10.049875621

Simplifying
x + 10 = -10.049875621

Reorder the terms:
10 + x = -10.049875621

Solving
10 + x = -10.049875621

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 = -10.049875621 + -10

Combine like terms: 10 + -10 = 0
0 + x = -10.049875621 + -10
x = -10.049875621 + -10

Combine like terms: -10.049875621 + -10 = -20.049875621
x = -20.049875621

Simplifying
x = -20.049875621

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.049875621, -20.049875621}
Solution
x = {0.049875621, -20.049875621}