 Okay, so we've got the same things a little bit. I wrote a little bit smaller so I can work Leave myself a little bit of room, right? so what we're gonna do is try to solve this equation and We're gonna solve this equation by cross-multiply this guy up here So what we're gonna do is grab this guy Grab this guy kick it out. So five times 6x is going to be 30x It's equal to 3x times 3x plus one so this guy comes up and multiplies both that term and that term so this is going to be 9x squared plus 3x Now again, I should have followed my own advice before we continue with this before we start moving things around We should have written down a restriction here and our restriction is 3x Cannot equals zero or and 6x cannot equal zero both of them State basically give us the result that x cannot equal zero Now keep that there because when you write your final answer you have to include that in your final answer So over here we're back over here. What I want to do is bring all the x's to one side Now what I'm going to do is I'm going to grab this guy and bring this to the other side because I want to keep my X squared first term positive. I rather not bring those guys over this side First term general positive So this is going to be now doesn't make a difference if I write this over here I'm right over here because this side is just going to be zero, right? So I'm going to line up my equals sign I'm going to have 9x square Plus when 30x comes over it becomes minus 30x so it becomes It's not a plus Shouldn't write it down until you solve for it actually. I'll tell you figure out what it is is minus 27x is equal to zero Okay Now we haven't talked about this, but we will talk about it later on at some point The way we have to solve this is take out a GCF the greatest common factor Now the GCF out of this basically we're factoring this right now. There's four types of factoring which is GCF Simple trinomial complex trinomes. We have a variable in front the x squared. This is a quadrat equation I'm going way beyond what we have what we've covered so far but this is just a sort of a pointer how we go about doing this a bit and And then there's the difference of squares, right? But we will talk about those later on now the way to solve this equation is we're going to take out a GCF here And the GCF from this greatest common factor is you have a 9 here you have a 27 If you take out a 9 from this you got one left if you can take out a 9 from this you get three left so the Greatest common factor from these is 9 to come out of this Okay, you have an x squared basically means you have two x's you got an x there So you can take out an x one single x for both of them. So you got 9x coming out, right? What you got left over is Yet if you multiply 9x by x you're gonna get not x squared so x You put x here and you're gonna put 3 over here equal to 0, right? Here's a property of Zero which we end up using when we're solving these types of equations Now with the problem of zero is our restrictions, right? one solution one tool that we can or one property that comes up with zero that we end up using is The only way to multiply two things or multiple things together to give you zero is that at least one of them has to be Now let's do an aside here I'm just gonna do this thing in pink because and I'm gonna talk about this a lot more later on But this is something that you know it's usually not talked about not introduced from what I've seen all the students that I've dealt with is Most people don't know how to why you separate these into two terms because what happens here is If you have 9x times 3 x minus 3 is equal to 0 What you do is the solution to this is you set each one of these equal to 0 and You know that the very behind this sort of or basically train of thought behind this is how could you multiply? a times b times c times d To give you zero how could you multiply four things to give you zero? The only way you multiply anything together to give you zero is that if at least one of them is zero now We don't know if it's a b c or d that's equal to zero or combination of each all of them or or all right, so what we do is we set each Term equal to zero so what we're gonna do is get an equation like this. We're gonna go And that's how we solve these types of equations. This is the same thing when we have two terms Multiplied together to give you zero What we do the way you solve for this is you set each one equal to zero so over here you would go nine x is equal to zero and over here you're gonna go x minus three is equal to zero And the solution to this is you just divide by nine and zero divided by nine is zero So your solution here is x is equal to zero and your solution here is just going to be you move the three over So x is equal to three Now over here we've got two solutions right Over here we've got two solutions But we really don't have two solutions because we have to look at our restriction When we set it up at the beginning of the equation and our restriction said x cannot equal zero Over here we put x equals zero but it can't equal zero so we find right the final solution for this Equation you're going to eliminate this answer x cannot equal zero so this doesn't exist So the only solution is x is equal to zero now what's going to happen is a lot of lot of lot of lot again lot of Schools that I've seen what they do is they get this type of problem and they say solve write about they say solve and Whenever they give you whenever they give you a question like this what they're usually going to do is say solve and check When they say this when you get to the final answer of the bottom over here There's a whole bunch of work that you have to do on the side or at the bottom of it to check the answer to this So let's do a check as well Just doing one question with the restrictions So over here your solution would have been x is equal to three and x cannot equal zero Right, that's our final solution to this now If we didn't write our restriction during the check This would have come up the x cannot equal zero would have come up because the answer would have been invalid So let's do a check for this question and see how that works out