360x=(x-5)(6x-360)

Solution for 360x=(x-5)(6x-360) equation:

Simplifying
360x = (x + -5)(6x + -360)

Reorder the terms:
360x = (-5 + x)(6x + -360)

Reorder the terms:
360x = (-5 + x)(-360 + 6x)

Multiply (-5 + x) * (-360 + 6x)
360x = (-5(-360 + 6x) + x(-360 + 6x))
360x = ((-360 * -5 + 6x * -5) + x(-360 + 6x))
360x = ((1800 + -30x) + x(-360 + 6x))
360x = (1800 + -30x + (-360 * x + 6x * x))
360x = (1800 + -30x + (-360x + 6x2))

Combine like terms: -30x + -360x = -390x
360x = (1800 + -390x + 6x2)

Solving
360x = 1800 + -390x + 6x2

Solving for variable 'x'.

Reorder the terms:
-1800 + 360x + 390x + -6x2 = 1800 + -390x + 6x2 + -1800 + 390x + -6x2

Combine like terms: 360x + 390x = 750x
-1800 + 750x + -6x2 = 1800 + -390x + 6x2 + -1800 + 390x + -6x2

Reorder the terms:
-1800 + 750x + -6x2 = 1800 + -1800 + -390x + 390x + 6x2 + -6x2

Combine like terms: 1800 + -1800 = 0
-1800 + 750x + -6x2 = 0 + -390x + 390x + 6x2 + -6x2
-1800 + 750x + -6x2 = -390x + 390x + 6x2 + -6x2

Combine like terms: -390x + 390x = 0
-1800 + 750x + -6x2 = 0 + 6x2 + -6x2
-1800 + 750x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-1800 + 750x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-300 + 125x + -1x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-300 + 125x + -1x2)' equal to zero and attempt to solve:

Simplifying
-300 + 125x + -1x2 = 0

Solving
-300 + 125x + -1x2 = 0

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

Divide each side by '-1'.
300 + -125x + x2 = 0

Move the constant term to the right:

Add '-300' to each side of the equation.
300 + -125x + -300 + x2 = 0 + -300

Reorder the terms:
300 + -300 + -125x + x2 = 0 + -300

Combine like terms: 300 + -300 = 0
0 + -125x + x2 = 0 + -300
-125x + x2 = 0 + -300

Combine like terms: 0 + -300 = -300
-125x + x2 = -300

The x term is -125x.  Take half its coefficient (-62.5).
Square it (3906.25) and add it to both sides.

Add '3906.25' to each side of the equation.
-125x + 3906.25 + x2 = -300 + 3906.25

Reorder the terms:
3906.25 + -125x + x2 = -300 + 3906.25

Combine like terms: -300 + 3906.25 = 3606.25
3906.25 + -125x + x2 = 3606.25

Factor a perfect square on the left side:
(x + -62.5)(x + -62.5) = 3606.25

Calculate the square root of the right side: 60.052060747

Break this problem into two subproblems by setting 
(x + -62.5) equal to 60.052060747 and -60.052060747.

Subproblem 1
x + -62.5 = 60.052060747

Simplifying
x + -62.5 = 60.052060747

Reorder the terms:
-62.5 + x = 60.052060747

Solving
-62.5 + x = 60.052060747

Solving for variable 'x'.

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

Add '62.5' to each side of the equation.
-62.5 + 62.5 + x = 60.052060747 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + x = 60.052060747 + 62.5
x = 60.052060747 + 62.5

Combine like terms: 60.052060747 + 62.5 = 122.552060747
x = 122.552060747

Simplifying
x = 122.552060747

Subproblem 2
x + -62.5 = -60.052060747

Simplifying
x + -62.5 = -60.052060747

Reorder the terms:
-62.5 + x = -60.052060747

Solving
-62.5 + x = -60.052060747

Solving for variable 'x'.

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

Add '62.5' to each side of the equation.
-62.5 + 62.5 + x = -60.052060747 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + x = -60.052060747 + 62.5
x = -60.052060747 + 62.5

Combine like terms: -60.052060747 + 62.5 = 2.447939253
x = 2.447939253

Simplifying
x = 2.447939253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {122.552060747, 2.447939253}
Solution
x = {122.552060747, 2.447939253}