x=x(60-2x)(45-2x)

Solution for x=x(60-2x)(45-2x) equation:

Simplifying
x = x(60 + -2x)(45 + -2x)

Multiply (60 + -2x) * (45 + -2x)
x = x(60(45 + -2x) + -2x * (45 + -2x))
x = x((45 * 60 + -2x * 60) + -2x * (45 + -2x))
x = x((2700 + -120x) + -2x * (45 + -2x))
x = x(2700 + -120x + (45 * -2x + -2x * -2x))
x = x(2700 + -120x + (-90x + 4x2))

Combine like terms: -120x + -90x = -210x
x = x(2700 + -210x + 4x2)
x = (2700 * x + -210x * x + 4x2 * x)
x = (2700x + -210x2 + 4x3)

Solving
x = 2700x + -210x2 + 4x3

Solving for variable 'x'.

Combine like terms: x + -2700x = -2699x
-2699x + 210x2 + -4x3 = 2700x + -210x2 + 4x3 + -2700x + 210x2 + -4x3

Reorder the terms:
-2699x + 210x2 + -4x3 = 2700x + -2700x + -210x2 + 210x2 + 4x3 + -4x3

Combine like terms: 2700x + -2700x = 0
-2699x + 210x2 + -4x3 = 0 + -210x2 + 210x2 + 4x3 + -4x3
-2699x + 210x2 + -4x3 = -210x2 + 210x2 + 4x3 + -4x3

Combine like terms: -210x2 + 210x2 = 0
-2699x + 210x2 + -4x3 = 0 + 4x3 + -4x3
-2699x + 210x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-2699x + 210x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2699 + 210x + -4x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-2699 + 210x + -4x2)' equal to zero and attempt to solve:

Simplifying
-2699 + 210x + -4x2 = 0

Solving
-2699 + 210x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
674.75 + -52.5x + x2 = 0

Move the constant term to the right:

Add '-674.75' to each side of the equation.
674.75 + -52.5x + -674.75 + x2 = 0 + -674.75

Reorder the terms:
674.75 + -674.75 + -52.5x + x2 = 0 + -674.75

Combine like terms: 674.75 + -674.75 = 0.00
0.00 + -52.5x + x2 = 0 + -674.75
-52.5x + x2 = 0 + -674.75

Combine like terms: 0 + -674.75 = -674.75
-52.5x + x2 = -674.75

The x term is -52.5x.  Take half its coefficient (-26.25).
Square it (689.0625) and add it to both sides.

Add '689.0625' to each side of the equation.
-52.5x + 689.0625 + x2 = -674.75 + 689.0625

Reorder the terms:
689.0625 + -52.5x + x2 = -674.75 + 689.0625

Combine like terms: -674.75 + 689.0625 = 14.3125
689.0625 + -52.5x + x2 = 14.3125

Factor a perfect square on the left side:
(x + -26.25)(x + -26.25) = 14.3125

Calculate the square root of the right side: 3.783186488

Break this problem into two subproblems by setting 
(x + -26.25) equal to 3.783186488 and -3.783186488.

Subproblem 1
x + -26.25 = 3.783186488

Simplifying
x + -26.25 = 3.783186488

Reorder the terms:
-26.25 + x = 3.783186488

Solving
-26.25 + x = 3.783186488

Solving for variable 'x'.

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

Add '26.25' to each side of the equation.
-26.25 + 26.25 + x = 3.783186488 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + x = 3.783186488 + 26.25
x = 3.783186488 + 26.25

Combine like terms: 3.783186488 + 26.25 = 30.033186488
x = 30.033186488

Simplifying
x = 30.033186488

Subproblem 2
x + -26.25 = -3.783186488

Simplifying
x + -26.25 = -3.783186488

Reorder the terms:
-26.25 + x = -3.783186488

Solving
-26.25 + x = -3.783186488

Solving for variable 'x'.

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

Add '26.25' to each side of the equation.
-26.25 + 26.25 + x = -3.783186488 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + x = -3.783186488 + 26.25
x = -3.783186488 + 26.25

Combine like terms: -3.783186488 + 26.25 = 22.466813512
x = 22.466813512

Simplifying
x = 22.466813512

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.033186488, 22.466813512}
Solution
x = {0, 30.033186488, 22.466813512}