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Chapter 5: Problem 4

Solve. $$(x-3)(x-2)=0$$

Short Answer

Expert verified
The solution to the equation is \(x = 3\) or \(x = 2\).

Step by step solution

01

Apply the Zero-Product Property

According to the zero-product property, if (x-3) multiplied by (x-2) equals zero, then either (x-3) equals zero or (x-2) equals zero. That is, each factor is set equal to zero. We write this as x-3 = 0 or x-2 = 0.
02

Solve for X

Next, Solve each equation independently to isolate x. For the first equation, x-3 = 0, to isolate x, add 3 to both sides to get x = 3. Similarly, for the second equation x-2 = 0, get x = 2 by adding 2 to both sides.

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