Given the law of composition x*y = 2xy - 6x - 6y + 21 solve the equation x*x*x = 3

We'll re-write the law of composition
as:

 2xy - 6x - 6y + 21 = 2(x-3)(y-3) +
3

Now, we'll apply the law of composition for
x*x:

x*x = 2(x-3)(x-3) + 3

x*x
= 2(x-3)^2 + 3

Now we'll solve
x*x*x:

[2(x-3)^2 + 3]*x = 2[2(x-3)^2 + 3 - 3](x-3) +
3

We'll eliminate like
terms:

4(x-3)^3 + 3 = 3

We'll
eliminate like terms:

4(x-3)^3 =
0

We'll divide by 4:

(x-3)^3 =
0

The solutions of the equation are: x1 = x2
= x3  = 3.