Solve each equation in Exercises 1 - 14 by factoring.

Question

2 x (x - 3) = 5 x^{2} - 7 x

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to solve the equation 78 times a minus four is equal to four A squared minus 21 A. So in this case you can see that my left hand side Has this seven a. That still needs to be distributed to the inside of the parentheses. So before I worry about factoring I'm going to make sure that all my terms are expanded. So 78 times A. Is seven A. Squared and 78 times negative four is negative 28 A. And my right hand side is still for a squared -218. So now I want to find the values of A by factoring which means that I need to combine all of my terms to one side. So I can then factor that one side. So I'm going to go ahead and add A. And subtract by negative seven A. Squared. If I do that to both sides My left hand side becomes zero and my right hand side is now four A squared minus seven A squared is negative three A squared And -21 a plus 28 day is seven a. So now I have this new equation negative three A squared plus seven eight that I can factor and in this case you can see that I have a terms or a values in both of my terms. So I can factor out with me and if I do that I'm left with a times negative three A plus seven. So now I have these two terms that I can use to solve for A. I have the a. And then I have the -3 a. Plus seven. So first I have A. Is equal to zero and there's not much else I can do with that. So A equals zero is one of the solutions And then I have negative three a. Plus seven is equal to zero. And I can sell for A. By subtracting by seven have negative three A. Is equal to negative seven And then dividing by -3. A. is equal to positive 7/3. And now this is my second solution for A. So now we've solved A. By factoring and we've gotten A equals zero and A equals seven divided by three. So you can see that that aligns with answer choice. B Many of these answer choices are very similar but it's important to note that these have different fraction values. So when you're choosing your answer be careful to make sure that it's the same one that we've solved for. So hopefully this video helped and see you next time

Solve each equation in Exercises 1 - 14 by factoring. $2 x (x - 3) = 5 x^{2} - 7 x$

Key Concepts

Factoring Quadratic Expressions

Setting the Equation to Zero

Zero-Product Property

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