Solve each equation in Exercises 1 - 14 by factoring.

3x^2 + 12x = 0

Question

Solve each equation in Exercises 1 - 14 by factoring.

3x^2 + 12x = 0

Accepted Answer

Hello, everyone. In this video, we're gonna be looking at this practice problem where we want to solve the value of Y in the equation four Y squared minus 36 Y is equal to zero and we're gonna solve it by factoring. So in this case, you can see that we have the variable Y present in both of the terms in both the 36 and the four. So that's telling me that I can factor out A Y from both of the terms. And you can also see that I can factor out a four from both terms because the first term has a four and if I take away four from 36 I'm left with nine. So if I factor four Y from both of these terms, my first term becomes Y because four Y times Y is four Y squared and my second term 36 Y becomes nine because four Y times negative nine is negative 36 Y. So you can see that by factoring it, I still get the same result. It's just now factored. So I have two terms, four Y and Y minus nine is equal to zero. So now that I have these two factors I can solve for them separately to find my solutions for Y. So I can say four, Y is equal to zero and Y minus nine is equal to zero. So solving for the first one, I get Y is equal to zero. And my second one, I'll add nine to both sides. So Y is equal to nine. So from here you can see that Y has two solutions, it could be zero or nine. So this becomes my final answer for the solutions of Y in this equation. And you can see that this aligns with answer choice D where Y is equal to zero and positive nine. So hopefully this video will help and see you next time.

Solve each equation in Exercises 1 - 14 by factoring. 3x^2 + 12x = 0

Verified Solution

Key Concepts

Factoring Quadratic Equations

Zero Product Property

Greatest Common Factor (GCF)