Question

$4b^2-60b+224=0$

Short answer

$$\begin{gathered} b=7, \\ b=8 \end{gathered}$$

Step-by-step solution

Step 1. Given information

$4b^2-60b+224=0$

Step 2. Finding common factor

$$\begin{gathered} 4b^2-60b+224=0 \\ 4(b^2-15b+56)=0 \end{gathered}$$

Step 3. Divide both sides by same factor

$$\begin{gathered} 4(b^2-15b+56)=0 \\ \frac{4(b^2-15b+56)}{4}=\frac{0}{4} \\ {b}^2-15b+56=0 \end{gathered}$$

Step 4. Factorization

$$\begin{gathered} b^2-15b+56=0 \\ {b}^2-8b-7b+56=0 \\ b(b-8)-7(b-8)=0 \\ (b-8)(b-7)=0 \end{gathered}$$

Step 5. Finding values

$(b-8)(b-7)=0$

So,

$$\begin{gathered} b-8=0 \\ b=8 \end{gathered}$$

Also,

$$\begin{gathered} b-7=0 \\ b=7 \end{gathered}$$