Question

In the following exercises, solve:

$6m(12m-5)=0$

Short answer

The solution is$m=\frac{5}{12}$.

Step-by-step solution

Step 1. Given Information 

The given expression is$6m(12m-5)=0$.

We have to solve the expression by using the Zero Product Property.

Step 2. Use the Zero Product Property 

If the product equals zero then at least one factor must equal zero.

So, we will put each factor equal to zero.

$$\begin{gathered} 6m(12m-5)=0 \\ 6m=0or12m-5=0 \end{gathered}$$

Step 3. Solve the linear equations  

The equation we get are

$$\begin{gathered} 6m=0 \\ 12m-5=0 \end{gathered}$$

Therefore,

localid="1661928752428" $$\begin{gathered} 6m=0 \\ m=\frac{0}{6} \\ m=0 \end{gathered}$$ or $$\begin{gathered} 12m-5=0 \\ m=\frac{5}{12} \end{gathered}$$

Step 4. Verify the answer

To verify the answer we will substitute the solution into the original equation.

If $m=\frac{5}{12}$

$$\begin{gathered} 6\left(\frac{5}{12}\right)\left[12\right(\frac{5}{12})-5]=0 \\ \frac{5}{2}[5-5]=0 \\ 0=0 \end{gathered}$$

Therefore, the solution is right.