SQL UPDATE two List Boxes w/ submit button

Question

Currently I have put together this page and it is working nicely and pulling the data, populating the list boxes, and allowing me to switch between the two. I put a submit button at the bottom that I want the user to click on and it will go ahead and update the SQL server with the changes. I can't seem to figure out how to do that.

I want to take each item in List1 and make sure the columns named account_number & date_installed are set to NULL in my tbl_assets table.

I want to take each item in List2 and make sure the columns named account_number=[JOBID] & date_installed=CURDATE() in my tbl_assets table.

After the updates are completed I want the user to be automatically redirected back to jobs.php page

<?php

$connection = mysql_connect('#', '#', '#');
mysql_select_db('#');

$techequipment = "SELECT serial, type_id FROM tbl_assets WHERE user_id = {$_GET ['TechID']} AND date_installed IS NULL AND date_returned IS NULL AND metro_date_returned IS NULL ORDER BY type_id, serial";
$techresult = mysql_query($techequipment);

$jobequipment = "SELECT serial, type_id FROM tbl_assets WHERE account_number = {$_GET ['JobNum']} ORDER BY type_id, serial";
$jobresult = mysql_query($jobequipment);
?>


<title>Assign Equipment</title>
<table align="center">

<tr>    
<td><center><b><?php echo "Tech #"; echo $_GET ['TechID']; echo " Assigned Equipment"; ?></b></center></td>`    
<td></td>   
<td><center><b><?php echo "Job #"; echo $_GET ['JobNum']; echo " Assigned Equipment"; ?></b></center></td>  
</tr>

<tr>
<td>
<select name="dynamic_data" size=20 multiple  id="list1" STYLE="width: 350px">
<?php $i=0; while($row = mysql_fetch_array($techresult)) { ?>
<option value="<?= $row["type_id"]." - ".$row["serial"];?>"><?=$row["type_id"]." - ".$row["serial"];?></option>
<?php $i++; } ?> </select>  
</td>

<td>
<center><input type="button" id="btnAdd" value="Transfer >>"/></center>
<center><input type="button" id="btnRemove" value="<< Transfer"/></center>
</td>

<td>
<select name="dynamic_data" size=20 multiple  id="list2" STYLE="width: 350px">
<?php $i=0; while($row = mysql_fetch_array($jobresult)) { ?>
<option value="<?= $row["type_id"]." - ".$row["serial"];?>"><?=$row["type_id"]." - ".$row["serial"];?></option>
<?php $i++; } ?> </select>  
</td>
</tr>

<tr>
<td>
<form action="jobs.php">
<center><input type="submit" value="EXIT"/></center>
</form>
</td>

<td>
</td>

<td>
<form action="assigned_equipment.php" method="post">
<center><input name="btnSubmit" type="submit" value="SUBMIT"/></center>
</form>
</td>
</tr>   
<tr>
<td colspan="3">
<center>Multi Select: Press & hold [CTRL] while clicking on the items.</center>
</td>
</tr>
</table>

<script src="js/jquery-2.2.0.js" type="text/javascript"></script>

<script type="text/javascript">
    $(document).ready(
        function () {

//TAKE EQUIPMENT FROM TECH AND PUT IT IN JOB BOX            
            $('#btnAdd').click(
                function (e) {
                    $('#list1 > option:selected').appendTo('#list2');
                    e.preventDefault();
                });


//TAKE EQUIPMENT FROM JOB AND PUT IT IN TECH BOX
                $('#btnRemove').click(
                function (e) {
                    $('#list2 > option:selected').appendTo('#list1');
                    e.preventDefault();
                });
        });
</script>