x(18-2x)(33-2x)=x

Solution for x(18-2x)(33-2x)=x equation:

Simplifying
x(18 + -2x)(33 + -2x) = x

Multiply (18 + -2x) * (33 + -2x)
x(18(33 + -2x) + -2x * (33 + -2x)) = x
x((33 * 18 + -2x * 18) + -2x * (33 + -2x)) = x
x((594 + -36x) + -2x * (33 + -2x)) = x
x(594 + -36x + (33 * -2x + -2x * -2x)) = x
x(594 + -36x + (-66x + 4x2)) = x

Combine like terms: -36x + -66x = -102x
x(594 + -102x + 4x2) = x
(594 * x + -102x * x + 4x2 * x) = x
(594x + -102x2 + 4x3) = x

Solving
594x + -102x2 + 4x3 = x

Solving for variable 'x'.

Reorder the terms:
594x + -1x + -102x2 + 4x3 = x + -1x

Combine like terms: 594x + -1x = 593x
593x + -102x2 + 4x3 = x + -1x

Combine like terms: x + -1x = 0
593x + -102x2 + 4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(593 + -102x + 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 '(593 + -102x + 4x2)' equal to zero and attempt to solve:

Simplifying
593 + -102x + 4x2 = 0

Solving
593 + -102x + 4x2 = 0

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

Divide each side by '4'.
148.25 + -25.5x + x2 = 0

Move the constant term to the right:

Add '-148.25' to each side of the equation.
148.25 + -25.5x + -148.25 + x2 = 0 + -148.25

Reorder the terms:
148.25 + -148.25 + -25.5x + x2 = 0 + -148.25

Combine like terms: 148.25 + -148.25 = 0.00
0.00 + -25.5x + x2 = 0 + -148.25
-25.5x + x2 = 0 + -148.25

Combine like terms: 0 + -148.25 = -148.25
-25.5x + x2 = -148.25

The x term is -25.5x.  Take half its coefficient (-12.75).
Square it (162.5625) and add it to both sides.

Add '162.5625' to each side of the equation.
-25.5x + 162.5625 + x2 = -148.25 + 162.5625

Reorder the terms:
162.5625 + -25.5x + x2 = -148.25 + 162.5625

Combine like terms: -148.25 + 162.5625 = 14.3125
162.5625 + -25.5x + x2 = 14.3125

Factor a perfect square on the left side:
(x + -12.75)(x + -12.75) = 14.3125

Calculate the square root of the right side: 3.783186488

Break this problem into two subproblems by setting 
(x + -12.75) equal to 3.783186488 and -3.783186488.

Subproblem 1
x + -12.75 = 3.783186488

Simplifying
x + -12.75 = 3.783186488

Reorder the terms:
-12.75 + x = 3.783186488

Solving
-12.75 + x = 3.783186488

Solving for variable 'x'.

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

Add '12.75' to each side of the equation.
-12.75 + 12.75 + x = 3.783186488 + 12.75

Combine like terms: -12.75 + 12.75 = 0.00
0.00 + x = 3.783186488 + 12.75
x = 3.783186488 + 12.75

Combine like terms: 3.783186488 + 12.75 = 16.533186488
x = 16.533186488

Simplifying
x = 16.533186488

Subproblem 2
x + -12.75 = -3.783186488

Simplifying
x + -12.75 = -3.783186488

Reorder the terms:
-12.75 + x = -3.783186488

Solving
-12.75 + x = -3.783186488

Solving for variable 'x'.

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

Add '12.75' to each side of the equation.
-12.75 + 12.75 + x = -3.783186488 + 12.75

Combine like terms: -12.75 + 12.75 = 0.00
0.00 + x = -3.783186488 + 12.75
x = -3.783186488 + 12.75

Combine like terms: -3.783186488 + 12.75 = 8.966813512
x = 8.966813512

Simplifying
x = 8.966813512

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.533186488, 8.966813512}
Solution
x = {0, 16.533186488, 8.966813512}