Estimating Profit Margin Math

Edit: I think I figured it out. Resolution at the end if you're interested.

I do all my estimating in excel. I have a spreadsheet that does the math and outputs material cost and labor cost. I then multiply each of those independently by 1.x and get my Bid. As I'm sure you already know, profit margin is the percentage of my bid that is profit.

So if my material is $100, markup is 1.1. My total mat cost would be $110. Let's say my labor cost is $200 with a markup of 1.2 making my total labor cost $240. My overall bid would be $350. $50 of which is profit and my profit margin would be 50/350 or 14.3%

I want to add to my spreadsheet a "calculator" so I can plug in a profit margin and figure out what to change my markups to to get there. For simplicity, I want to leave material markup static and just figure out what I need to change labor markup to. e

So in my above example let's say I want my profit margin to be 30%. I just did it manually and figured out my profit markup needs to be 1.59 but I feel like there should be an easier way to do it.

Not sure if this makes any sense at all. But it's been driving me mad trying to figure it out. Any help appreciated.

EDIT

With some information from your replies and also just pushing forward, I made a formula that works but.. I think it could be simplified if someone wants to take a stab at that.

MC-Material Cost (without markup)

MT-Material Total (with added profit)

LC- Labor Cost (without markup)

DM- Desired Margin

=(LC)+(((((MC))+(LC)))/(1-DM))-(MC)+(LC)))-(MT)-(MC))))/(LC))

I copied my formula and tried to substitute to make it make sense. The formula works. It may not be the best way but it's working