Question

In the following exercises, solve.

$(x-3)(x+7)=0$

Short answer

The solution is$x=3,-7.$

Step-by-step solution

Step 1. Given Information.

The given equation is$(x-3)(x+7)=0$

Step 2. Solution of the equation.

Using the Zero Product Property,

$$\begin{gathered} x-3=0 \\ x=3 \\ Also, \\ x+7=0 \\ x=-7 \end{gathered}$$

Step 3. Checking the solution

On substituting $x=3$,

$$\begin{gathered} (3-3)(x+7)=0 \\ 0(x+7)=0 \\ 0=0 \end{gathered}$$

which is true.

On substituting $x=-7,$

$$\begin{gathered} (x-3)(-7+7)=0 \\ (x-3)\left(0\right)=0 \\ 0=0 \end{gathered}$$

which is true.