Question

In the following exercises, solve.

$(3a-10)(2a-7)=0$

Short answer

The solution is$a=\frac{10}{3},\frac{7}{2}$.

Step-by-step solution

Step 1. Given Information.

The given equation is ,

$(3a-10)(2a-7)=0$

Step 2. Solution of the equation.

Using the Zero product property,

$$\begin{gathered} (3a-10)(2a-7)=0 \\ \Rightarrow 3a-10=0 \\ \Rightarrow a=\frac{10}{3} \\ \Rightarrow 2a-7=0 \\ \Rightarrow a=\frac{7}{2} \end{gathered}$$

Step 3. Check the solution.

Substitute $a=\frac{10}{3},$

$$\begin{gathered} (3\times \frac{10}{3}-10)(2a-7)=0 \\ \left(0\right)(2a-7)=0 \\ 0=0 \end{gathered}$$

which is true.

Now, Substitute $a=\frac{7}{2},$

$$\begin{gathered} (3a-10)(2\times \frac{7}{2}-7)=0 \\ (3a-10)\left(0\right)=0 \\ 0=0 \end{gathered}$$

which is true.