Question

Solve:

$w(2w+3)=0$

Short answer

By solving the equation $w(2w+3)=0$, the value of w is $w=0,-\frac{3}{2}$

Step-by-step solution

Step 1. Given Information

An equation:

$w(2w+3)=0$

Step 2. Use the Zero-Product property

Use the Zero Product Property to set each factor to zero.
$$\begin{gathered} w=0; \\ 2w+3=0 \end{gathered}$$

Step 3. Solve the equations

$w=0$

And

$$\begin{gathered} 2w+3=0 \\ 2w=-3 \\ w=-\frac{3}{2} \end{gathered}$$

The values of w is $w=0,-\frac{3}{2}$

Step 4. Check the answer

Check by substituting the values in the original equation,
When $w=0$,

$$\begin{gathered} w(2w+3)=0 \\ 0\left(2\right(0)+3)=0 \\ 0=0 \end{gathered}$$

When $w=-\frac{3}{2}$,

$$\begin{gathered} -\frac{3}{2}\left(2\right(\frac{-3}{2})+3)=0 \\ -\frac{3}{2}(\_3+3)=0 \\ \frac{-3}{2}\left(0\right)=0 \\ 0=0 \end{gathered}$$

Hence the equation is true.