Determine the neutral element of the law of composition xy

Determine the neutral element of the law of composition x*y = 3xy + 6(x+y) + 10

We have to determine the neutral element for x*y = 3xy + 6(x+y) + 10

To find this, let the neutral element be N, now x*N = e*N = x

From the given expression:

x*N = 3xN + 6(x+N) + 10

As this is also equal to x

=>3xN + 6(x+N) + 10 = x

=> 3xN + 6x + 6N + 10 = x

=> 3xN + 6N = x - 6x - 10

=> 3xN + 6N = -5x - 10

=> 3N ( x + 2) = -5x - 10

=> 3N ( x + 2) = -5 (x + 2)

=> 3N = -5

=> N = -5/3

So the neutral element is -5 /3.