Please derive the demand functions for the utility function U=a(x) + b(z) + xz. Then given a=2, b=3, price of x=1, price of z=2, and Y =50 find optimal values of x and z.

I believe the utility function is: U=2(x) +3(z) +xz

and budget constraint is: 50 = 1(x) + 2(z)

I tried the Lagrangian but I cannot get x or z alone

thank you for your time