Question

Solve:$123b=-6-60b^2$

Short answer

The answer is$b=\frac{1}{20},2.$

Step-by-step solution

Step 1. Given Information.

The given equation is$123b=-6-60b^2.$

Step 2. Factor the equation.

First, Factor the greatest common factor,

$$\begin{gathered} 123b=-6-60b^2 \\ =60b^2-123b+6=0 \\ =3(20b^2-41b+2)=0 \end{gathered}$$

Now,

Factor the trinomial,

$$\begin{gathered} 3(20b^2-40b-b+2)=0 \\ 3\left\{20b\right(b-2)-1(b-2\left)\right\}=0 \\ 3\left\{\right(20b-1\left)\right(b-2\left)\right\}=0 \end{gathered}$$

Step 3. Solution of the equation.

Use the Zero Product Property to set each factor to $0.$

Therefore,

$$\begin{gathered} 20b-1=0 \\ b=\frac{1}{20} \\ b-2=0 \\ b=2 \end{gathered}$$