Learning about CBM-BASIC

I've been solving Brilliant math problems with the simplest of BASIC programming languages lately. I do this because it's super convenient for me to write a quick little program to do some equation solving. CBM-BASIC is pretty nice for this because it works with Windows and Linux and my iPhone (by installing Hand-BASIC).

For a nice little example I solved this problem:

 With the help of Mathematica and CBM-BASIC. I used Mathematica to solve for z and plot the resulting equation to help me understand if there were a finite number of solutions. I was being lazy, because I could have figured this out just by plugging a few exploratory numbers in for X,Y, and Z to help me understand the bounds of the problem. Once I understood the bounds of the problem I was able to find all the solutions with CBM-BASIC in a relatively short time period.

Here is the resulting BASIC program:

10 REM Solve Brilliant Problem 2 of May 8, 2017 
20 S = 0
30 E1 = 0
40 MX = 150
50 MY = 50
60 MZ = 40
65 PRINT "FINDING SOLUTIONS..."
70 FOR X = 4 TO MX
80 FOR Y = 1 TO MY
90 FOR Z = 1 TO MZ
100 GOSUB 500
110 IF ABS(E1) < 0.1 THEN S=S+X+Y+Z : PRINT "S = ";S
120 NEXT Z : NEXT Y : NEXT X
130 PRINT "DONE." : END
500 REM EVALUATE FUNCTION E1
510 E1 = X^2*(Y^3+Z^3)-315*(X*Y*Z+7)
520 RETURN

And there you have it. I'll let the reader build CBM-BASIC and find the solution themselves. I'm having a lot of fun using this little Commordore 64 BASIC 2 implementation for my mental exercise. Who said BASIC causes brain damage?