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Chapter 5: Problem 3

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

Short Answer

Expert verified
The solution to the equation \( (x-2)(x+3)=0 \) are \( x=2 \) and \( x=-3 \).

Step by step solution

01

Set the first factor equal to zero

The first step to solving this equation is to set the first factor, \(x-2=0\), equal to zero. When \(x-2=0\), solve the equation for \(x\).
02

Solving for x

Adding 2 to both the sides of the equation \(x-2=0\) results \(x=2\). Hence, the first solution has been achieved.
03

Set the second factor equal to zero

The next step to solving this equation is to set the second factor, \(x+3=0\), equal to zero. Now again, when \(x+3=0\), solve the equation for \(x\).
04

Finding the Second Solution

Subtracting 3 from both the sides of the equation \(x+3=0\) results \(x=-3\). Therefore, the second solution is found.

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