Question Video: Solving Cubic Equations Written in Factorized Form

Solve the equation (3π‘₯ βˆ’ 2)(5π‘₯ + 2)(7π‘₯ βˆ’ 3) = 0.

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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, we’re going to use the fact that if we have two values π‘Ž and 𝑏 and their product is equal to zero, then π‘Ž equals zero or 𝑏 equals zero, or π‘Ž and 𝑏 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.

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