Question

Solve:

$2u(5u-1)=0$

Short answer

By solving the equation $2u(5u-1)=0$, the value of uis $u=0,\frac{1}{5}$

Step-by-step solution

Step 1. Given Information

An equation:

$2u(5u-1)=0$

Step 2. Use the Zero-Product property

Use the Zero Product Property to set each factor to zero.

$$\begin{gathered} 2u=0; \\ 5u-1=0 \end{gathered}$$

Step 3. Solve the equations

$$\begin{gathered} 2u=0 \\ u=0 \end{gathered}$$

And

$$\begin{gathered} 5u-1=0 \\ 5u=1 \\ u=\frac{1}{5} \end{gathered}$$

The value of u is $u=0,\frac{1}{5}$

Step 4. Check the answer

Check by substituting the values in the original equation,

When $u=0$,

$$\begin{gathered} 2\left(0\right)\left(5\right(0)-1)=0 \\ 0(-1)=0 \\ 0=0 \end{gathered}$$

When $u=\frac{1}{5}$,

$$\begin{gathered} 2\left(\frac{1}{5}\right)\left(5\right(\frac{1}{5})-1)=0 \\ \frac{2}{5}(1-1)=0 \\ 0=0 \end{gathered}$$

Hence the equation is true.