Question

Solve: $(x-3)(x+5)=0.$

Short answer

The solutions are$x=3orx=-5.$

Step-by-step solution

Step 1. Given Information

The given equation is $\left(x-3\right)\left(x+5\right)=0.$We have to solve it.

Step 2. Set each factor equal to zero

As it is given the product is equal to zero. So, at least one factor must equal zero.

$$\begin{gathered} \left(x-3\right)\left(x+5\right)=0 \\ x-3=0orx+5=0 \end{gathered}$$

Step 3. Solve the linear equations

Let's solve each equation

$$\begin{gathered} x-3=0orx+5=0 \\ x=3orx=-5 \end{gathered}$$

Step 4. Check the answer

To check the answer substitute values of xinto the original equation.

When $x=3$

$$\begin{gathered} \left(x-3\right)\left(x+5\right)=0 \\ \left(3-3\right)\left(3+5\right)=0 \\ 0\left(8\right)=0 \\ 0=0 \end{gathered}$$

It is true.

When $x=-5$

$$\begin{gathered} \left(x-3\right)\left(x+5\right)=0 \\ \left(-5-3\right)\left(-5+5\right)=0 \\ \left(-8\right)\left(0\right)=0 \\ 0=0 \end{gathered}$$

It is true.