180=60(x+20)3x

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

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

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

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

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

Solving
180 = 3600x + 180x2

Solving for variable 'x'.

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

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

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

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

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

Simplifying
1 + -20x + -1x2 = 0

Solving
1 + -20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 20x + x2 = 0

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}