Question

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

Short answer

The solutions to the equation \( (x-3)(x-2)=0 \) are \( x=2 \) and \( x=3 \)

Step-by-step solution

Set Each Factor Equals to Zero

We know that if a product of factors is zero, then one or both of the factors must be zero. So, we set each factor in the equation \( (x-3)(x-2)=0 \) equals to zero: that is, \(x-3=0\) and \(x-2=0\).

Solve for x

Now, solve each equation for \(x\). For \(x-3=0\), add 3 to both sides to find that \(x=3\). For \(x-2=0\), add 2 to both sides to find that \(x=2\). These are the solutions to the equation.