The product of one more than a number and 4 less than the number is 24. Find the number(s)!
Let \(x\) be a number,
\begin{equation*}
\begin{split}
(x + 1)\times (x - 4) &= 24\\\\
x^2 - 4x + x - 4 & = 24\\\\
x^2 - 3x - 4 - 24& = 0\\\\
x^2 - 3x - 28& = 0\:\:\:\:\:\color{blue}\text{(factorize)}\\\\
(x - 7)(x + 4) &= 0\\\\
x - 7 = 0 &\rightarrow x_1 = 7\\\\
x + 4 = 0 &\rightarrow x_2 = -4\\\\\\
\text{Then, the numbers are −4 or 7}
\end{split}
\end{equation*}
