Passes one test case :)

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1125392

use strict;

my @stack;
$_ = @ARGV ? "@ARGV" : '2 4x*8-*3x*+11x*1+9--'; # x cancels out
$_ = @ARGV ? "@ARGV" : '2 4x*8-*3x*+10x*1+9--'; # adjusted
print "    raw  $_\n";

use Data::Dump qw(pp);

while( /(\d+)|(x)|([*+-])/g )
  {
  pp \@stack;
  if( length $1 )
    {
    push @stack, [ $1 ];
    }
  elsif( $2 )
    {
    push @stack, [ 0, 1 ];
    }
  else
    {
    my $op = $3;
    my ($x, $y) = splice @stack, -2;
    if( $op eq '+' )
      {
      my $i = 0;
      $x->[$i++] += $_ for @$y;
      push @stack, $x;
      }
    elsif( $op eq '-' )
      {
      my $i = 0;
      $x->[$i++] -= $_ for @$y;
      push @stack, $x;
      }
    elsif( $op eq '*' )
      {
      push @stack, multiply( $x, $y );
      }
    }
  }

pp \@stack;
my ($x0, $x1) = @{ pop @stack };
if( $x1 )
  {
  print "x = ", -$x0 / $x1, "\n";
  }
else
  {
  die "x has cancelled out";
  }

sub multiply # two polynomials
  {
  my ($x, $y) = @_;
  my ($n, @result) = (0);
  for my $xval (@$x)
    {
    my $pos = $n;
    $result[$pos++] +=  $xval * $_ for @$y;
    $n++;
    }
  return \@result;
  }
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