216.75=(x-6)(x-6)(3)

Solution for 216.75=(x-6)(x-6)(3) equation:

Simplifying
216.75 = (x + -6)(x + -6)(3)

Reorder the terms:
216.75 = (-6 + x)(x + -6)(3)

Reorder the terms:
216.75 = (-6 + x)(-6 + x)(3)

Reorder the terms for easier multiplication:
216.75 = 3(-6 + x)(-6 + x)

Multiply (-6 + x) * (-6 + x)
216.75 = 3(-6(-6 + x) + x(-6 + x))
216.75 = 3((-6 * -6 + x * -6) + x(-6 + x))
216.75 = 3((36 + -6x) + x(-6 + x))
216.75 = 3(36 + -6x + (-6 * x + x * x))
216.75 = 3(36 + -6x + (-6x + x2))

Combine like terms: -6x + -6x = -12x
216.75 = 3(36 + -12x + x2)
216.75 = (36 * 3 + -12x * 3 + x2 * 3)
216.75 = (108 + -36x + 3x2)

Solving
216.75 = 108 + -36x + 3x2

Solving for variable 'x'.

Combine like terms: 216.75 + -108 = 108.75
108.75 + 36x + -3x2 = 108 + -36x + 3x2 + -108 + 36x + -3x2

Reorder the terms:
108.75 + 36x + -3x2 = 108 + -108 + -36x + 36x + 3x2 + -3x2

Combine like terms: 108 + -108 = 0
108.75 + 36x + -3x2 = 0 + -36x + 36x + 3x2 + -3x2
108.75 + 36x + -3x2 = -36x + 36x + 3x2 + -3x2

Combine like terms: -36x + 36x = 0
108.75 + 36x + -3x2 = 0 + 3x2 + -3x2
108.75 + 36x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
108.75 + 36x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-36.25 + -12x + x2 = 0

Move the constant term to the right:

Add '36.25' to each side of the equation.
-36.25 + -12x + 36.25 + x2 = 0 + 36.25

Reorder the terms:
-36.25 + 36.25 + -12x + x2 = 0 + 36.25

Combine like terms: -36.25 + 36.25 = 0.00
0.00 + -12x + x2 = 0 + 36.25
-12x + x2 = 0 + 36.25

Combine like terms: 0 + 36.25 = 36.25
-12x + x2 = 36.25

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 36.25 + 36

Reorder the terms:
36 + -12x + x2 = 36.25 + 36

Combine like terms: 36.25 + 36 = 72.25
36 + -12x + x2 = 72.25

Factor a perfect square on the left side:
(x + -6)(x + -6) = 72.25

Calculate the square root of the right side: 8.5

Break this problem into two subproblems by setting 
(x + -6) equal to 8.5 and -8.5.

Subproblem 1
x + -6 = 8.5

Simplifying
x + -6 = 8.5

Reorder the terms:
-6 + x = 8.5

Solving
-6 + x = 8.5

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 8.5 + 6

Combine like terms: -6 + 6 = 0
0 + x = 8.5 + 6
x = 8.5 + 6

Combine like terms: 8.5 + 6 = 14.5
x = 14.5

Simplifying
x = 14.5

Subproblem 2
x + -6 = -8.5

Simplifying
x + -6 = -8.5

Reorder the terms:
-6 + x = -8.5

Solving
-6 + x = -8.5

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -8.5 + 6

Combine like terms: -6 + 6 = 0
0 + x = -8.5 + 6
x = -8.5 + 6

Combine like terms: -8.5 + 6 = -2.5
x = -2.5

Simplifying
x = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.5, -2.5}