5x(180-x)=300

Solution for 5x(180-x)=300 equation:

Simplifying
5x(180 + -1x) = 300
(180 * 5x + -1x * 5x) = 300
(900x + -5x2) = 300

Solving
900x + -5x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + 900x + -5x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 900x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-60 + 180x + -1x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-60 + 180x + -1x2)' equal to zero and attempt to solve:

Simplifying
-60 + 180x + -1x2 = 0

Solving
-60 + 180x + -1x2 = 0

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

Divide each side by '-1'.
60 + -180x + x2 = 0

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -180x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + -180x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -180x + x2 = 0 + -60
-180x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
-180x + x2 = -60

The x term is -180x.  Take half its coefficient (-90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
-180x + 8100 + x2 = -60 + 8100

Reorder the terms:
8100 + -180x + x2 = -60 + 8100

Combine like terms: -60 + 8100 = 8040
8100 + -180x + x2 = 8040

Factor a perfect square on the left side:
(x + -90)(x + -90) = 8040

Calculate the square root of the right side: 89.666047086

Break this problem into two subproblems by setting 
(x + -90) equal to 89.666047086 and -89.666047086.

Subproblem 1
x + -90 = 89.666047086

Simplifying
x + -90 = 89.666047086

Reorder the terms:
-90 + x = 89.666047086

Solving
-90 + x = 89.666047086

Solving for variable 'x'.

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

Add '90' to each side of the equation.
-90 + 90 + x = 89.666047086 + 90

Combine like terms: -90 + 90 = 0
0 + x = 89.666047086 + 90
x = 89.666047086 + 90

Combine like terms: 89.666047086 + 90 = 179.666047086
x = 179.666047086

Simplifying
x = 179.666047086

Subproblem 2
x + -90 = -89.666047086

Simplifying
x + -90 = -89.666047086

Reorder the terms:
-90 + x = -89.666047086

Solving
-90 + x = -89.666047086

Solving for variable 'x'.

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

Add '90' to each side of the equation.
-90 + 90 + x = -89.666047086 + 90

Combine like terms: -90 + 90 = 0
0 + x = -89.666047086 + 90
x = -89.666047086 + 90

Combine like terms: -89.666047086 + 90 = 0.333952914
x = 0.333952914

Simplifying
x = 0.333952914

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {179.666047086, 0.333952914}
Solution
x = {179.666047086, 0.333952914}