The floor of a hall is a rectangle 4 m longer than it is wide…

Step 1. Equation. $w(w + 4) = 192$, so $w^2 + 4w - 192 = 0$.

Step 2. Factorise. $16 \times (-12) = -192$ and $16 - 12 = 4$, so $(w + 16)(w - 12) = 0$.

Step 3. Meaning. $w = 12$ or $w = -16$. A width is positive, so $w = 12\ \text{m}$.

Step 4. Check. The length is $16\ \text{m}$, and $12 \times 16 = 192\ \text{m}^2$.