(80-x)3x=180

Solution for (80-x)3x=180 equation:

Simplifying
(80 + -1x) * 3x = 180

Reorder the terms for easier multiplication:
3x(80 + -1x) = 180
(80 * 3x + -1x * 3x) = 180
(240x + -3x2) = 180

Solving
240x + -3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 240x + -3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 240x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 80x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-60 + 80x + -1x2)' equal to zero and attempt to solve:

Simplifying
-60 + 80x + -1x2 = 0

Solving
-60 + 80x + -1x2 = 0

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

Divide each side by '-1'.
60 + -80x + x2 = 0

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -80x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + -80x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -80x + x2 = 0 + -60
-80x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
-80x + x2 = -60

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = -60 + 1600

Reorder the terms:
1600 + -80x + x2 = -60 + 1600

Combine like terms: -60 + 1600 = 1540
1600 + -80x + x2 = 1540

Factor a perfect square on the left side:
(x + -40)(x + -40) = 1540

Calculate the square root of the right side: 39.242833741

Break this problem into two subproblems by setting 
(x + -40) equal to 39.242833741 and -39.242833741.

Subproblem 1
x + -40 = 39.242833741

Simplifying
x + -40 = 39.242833741

Reorder the terms:
-40 + x = 39.242833741

Solving
-40 + x = 39.242833741

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = 39.242833741 + 40

Combine like terms: -40 + 40 = 0
0 + x = 39.242833741 + 40
x = 39.242833741 + 40

Combine like terms: 39.242833741 + 40 = 79.242833741
x = 79.242833741

Simplifying
x = 79.242833741

Subproblem 2
x + -40 = -39.242833741

Simplifying
x + -40 = -39.242833741

Reorder the terms:
-40 + x = -39.242833741

Solving
-40 + x = -39.242833741

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = -39.242833741 + 40

Combine like terms: -40 + 40 = 0
0 + x = -39.242833741 + 40
x = -39.242833741 + 40

Combine like terms: -39.242833741 + 40 = 0.757166259
x = 0.757166259

Simplifying
x = 0.757166259

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {79.242833741, 0.757166259}
Solution
x = {79.242833741, 0.757166259}