Question

Solve:$\left(4p+3\right)\left(4p-3\right)=0.$

Short answer

The solutions are $p=-\frac{3}{4}orp=\frac{3}{4}.$

Step-by-step solution

Step 1. Given Information  

The given equation is$\left(4p+3\right)\left(4p-3\right)=0.$

We have to solve it.

Step 2. Use the zero product property

To solve the equation, we will use the Zero Product Property to set

each factor to zero.

$$\begin{gathered} \left(4p+3\right)\left(4p-3\right)=0 \\ 4p+3=0 \\ 4p-3=0 \end{gathered}$$

Step 3. Solve the equations

Let's solve each equation

$$\begin{gathered} 4p+3=0or4p-3=0 \\ 4p=-3or4p=3 \\ p=-\frac{3}{4}orp=\frac{3}{4} \end{gathered}$$

Step 4. Check the answer

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

When $p=-\frac{3}{4}$

$$\begin{gathered} \left(4p+3\right)\left(4p-3\right)=0 \\ \left\{4\left(-\frac{3}{4}\right)+3\right\}\left\{4\left(-\frac{3}{4}\right)-3\right\}=0 \\ \left(-3+3\right)\left(-3-3\right)=0 \\ 0\left(-6\right)=0 \\ 0=0 \end{gathered}$$

It is true.

When $m=\frac{3}{4}$

$$\begin{gathered} \left(4p+3\right)\left(4p-3\right)=0 \\ \left\{4\left(\frac{3}{4}\right)+3\right\}\left\{4\left(\frac{3}{4}\right)-3\right\}=0 \\ \left(3+3\right)\left(3-3\right)=0 \\ \left(6\right)\left(0\right)=0 \\ 0=0 \end{gathered}$$

It is true.