Here is the loop structure to your problem:

use strict;

my @list = (-25, 14, 50, 20, -7, -8, -10);
my @result = (); 
my $sum;
for my $elem (@list) {
    for (@{[@result]}) {
        push @result, [ @$_, $elem ];
        $sum = eval join '+' => @{$result[-1]};
        print join(',', @{$result[-1]}), "\n" unless $sum; 
    }
    push @result, [ $elem ];
    print $elem, "\n" unless $elem;
}
[download]

Result:

-25,50,-7,-8,-10

You will need some additional work in order to obtain array indexes instead of values.

How it works:

In first pass, it will ignore the inner for and it will push [ -25 ] into @result. Result is [ [-25] ]

In second pass, it will push 14 into a copy of what it already has, and then it will push [ 14 ]. Result is: [ [-25], [-25,14], [14] ]

In second pass, it will push 50 into a copy of what it already has, and then it will push [ 50 ]. Result is: [ [-25], [-25,14], [14], [-25,50], [-25,14,50], [14,50], [50] ]

While it does that, it will print whatever combinations that sum zero.

That's it!