Question

In the following exercises, solve.

$2x(6x-3)=0$

Short answer

The solution is$x=0,\frac{1}{2}$.

Step-by-step solution

Step 1. Given Information.

The given equation is$2x(6x-3)=0$.

Step 2. Solution of the equation.

Using the Zero product property,

$$\begin{gathered} 2x(6x-3)=0 \\ 2x=0;6x-3=0 \\ x=0;x=\frac{3}{6} \\ x=0,x=\frac{1}{2} \end{gathered}$$

Step 3. Check the solution.

Substitute $x=0$in the given equation,

$$\begin{gathered} (2\times 0)(6\times 0-3)=0 \\ 0\times -3=0 \\ 0=0 \end{gathered}$$

which is true.

Now, substitute $x=\frac{1}{2},$

$$\begin{gathered} 2\times \frac{1}{2}(6\times \frac{1}{2}-3)=0 \\ 1\left(0\right)=0 \\ 0=0 \end{gathered}$$

which is true.