### Video Transcript

Solve the equation three π₯ minus two five π₯ plus two seven π₯ minus three equals zero.

Here, we have three expressions multiplied together to give zero. So, we need to find a value of π₯ that will make the product of these expressions equal to zero. To do this, weβre going to use the fact that if we have two values π and π and their product is equal to zero, then π equals zero or π equals zero, or π and π equals zero. Looking at our equation then, it means that three π₯ minus two equals zero, or five π₯ plus two equals zero, or seven π₯ minus three equals zero.

Looking at three π₯ minus two equals zero, we can rearrange this by adding two to both sides to tell us that three π₯ equals two. To find π₯, we would then divide both sides of our equation by three. So, one solution to our equation would be π₯ equals two-thirds. When five π₯ plus two equals zero, then five π₯ would be equal to negative two. And so, π₯ would be equal to negative two-fifths. To find our final solution, when seven π₯ minus three would be equal to zero, then seven π₯ equals three. Therefore, π₯ equals three-sevenths. So, our final answer to the solution of the equation is π₯ equals two-thirds, π₯ equals negative two-fifths, and π₯ equals three-sevenths.