 So the next thing we ought to consider are multivariable equations. So a multivariable equation is an equation that involves more than one variable. So we can solve these equations for one of the variables in pretty much the same way that we solve any other equation. So we can identify the type of expression that we have, apply the same operation to both sides based on our expression, and when the equation is rewritten so that we have one variable as an expression of the others, we have the equation solved for that variable. And it helps to focus on the operations that specifically involve the variable of interest. All other operations are not really that important except for bookkeeping purposes. So for example, let's say I want to solve for R of t in this multivariable equation. One of R of t equals one of R of 1 plus one over R of 2. So R of 1, R of 2, R of t, these are all variables. I want to solve for R of t. Now the variable of interest is R of t. So I really don't care that over here I have one divided by R of 1, one divided by R of 2. I have a sum. What I really care about is that over on the left hand side, R of t is a divisor. So first of all, because it's a divisor, because it's in the denominator of some fraction, it can't be equal to zero, so I'll make a note of that. Next, the thing to observe is that I am dividing by R of t. Again, I don't really care what I'm doing with R of 1 and R of 2. I am interested in solving for R of t. I'm dividing by R of t, so I can multiply by it to undo that operation. So I'll multiply both sides by R of t. Parentheses are cheap. Don't forget to use them. R of t is being multiplied by everything over on the right hand side. And I can do a little bit of cancellation. And, well, a little analysis goes a long way. Again, I want to solve for R of t. And here I have R of t times some other factor. And what that means is I don't really care again what's going on in here, as long as it doesn't involve the variable I'm trying to solve for. This is R of t times something. And since I want to solve for R of t, I can divide by that factor. So R of t is 1 over this factor here. And I have that equation. And because this is now in the form R of t equals stuff that doesn't include R of t, this is now solved for R of t. Well, let's take a look at a different problem. We want to solve this equation for k. And note that k appears in this term and also in this term. So what I might want to do is I might want to start by isolating the k term. So the left-hand side of the equation, this side of the equation, there's a k term here. It's added. So I might want to get rid of any non-k terms by a subtraction. So there's my equation. I have an addition over on the left-hand side. So I will undo the addition by subtracting. And that gets rid of the 3x squared. So I have all on the right left-hand side just k terms. On the right, I have a k term as well. So I want to eliminate them from the right-hand side. So I have k terms on the left. I want to not have k terms on the right. And I'm adding over on the right-hand side so I can get rid of them by subtracting. So I'll subtract the xk. And so cleaning up, this is what I have left over on the right-hand side. Over on the left-hand side, I have 3y squared k minus xk. Now, it might not be obvious what to do next. So here's a reusable rule of thumb. And as much as I hate reducing mathematics to jingles, here's a nice one that actually turns out to be useful. If in doubt, factor or multiply out. If you're not sure what to do next, if you ever get stuck on a problem, try factoring or multiplying something out. Now, what this does requires you have to be able to identify which of these two things you can do. And the thing to notice here, again, we don't care about anything except for the k terms. The terms involving k are subtracted. And that means that I can apply the distributive property and factor. Remember, factoring changes an addition or subtraction into a multiplication. And I have an addition or subtraction. I have subtraction here, so I can factor. And I'll factor a k out. And that gets me this expression there. And, well, now it's clear that what's going on. Again, I'm trying to solve for k. I now have k times something that doesn't involve k. So I can divide by it. So I'll divide by that factor 3y squared minus x. And that will eliminate it from the left-hand side. And I'll have k equal 2. And again, I have this expression that does not involve k. So I have solved the equation for k.