You've got a couple of issues there. By making it a bit simpler, and adding the /g (global match) flag, it seems to work.

The ^ means match only at the beginning of the string, so you'll only get a single match, even with global flag set, and the (?:) non-capture grouping isn't required.

my $equation = '979x + 87y - 8723z = 274320';

# catch anything that proceeds an x, y or z, and then
# catch that letter as well into another capture group

my @parts = ($equation =~ /(.*?)([xyz])/ig);

print "$_\n" for @parts;
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Output:

979
x
 + 87
y
 - 8723
z
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