Question

In the following exercises, solve.

$(5b+1)(6b+1)=0$

Short answer

The solution is $b=\frac{-1}{5},\frac{-1}{6}$.

Step-by-step solution

Step 1. Given Information.

The given equation is$(5b+1)(6b+1)=0$.

Step 2. Solution of the equation

Using the Zero product property,

$$\begin{gathered} (5b+1)(6b+1)=0 \\ \Rightarrow 5b+1=0 \\ b=\frac{-1}{5} \\ \Rightarrow 6b+1=0 \\ b=\frac{-1}{6} \end{gathered}$$

Step 3. Check the solution.

Substitute $b=-\frac{1}{5},$

$$\begin{gathered} (5\times \frac{-1}{5}+1)(6b+1)=0 \\ \left(0\right)(6b+1)=0 \\ 0=0 \end{gathered}$$

which is true.

Now, Substitute $b=\frac{-1}{6},$

$$\begin{gathered} (5b+1)(6\times \frac{-1}{6}+1)=0 \\ (5b+1)\left(0\right)=0 \\ 0=0 \end{gathered}$$

which is true.