Computational and analytical problems with solutions in a two$-$column format

For the following function, find all intervals on which the function is positive and all intervals on which the function is negative. Include a detailed explanation for each step written in grammatically correct complete sentences within a two$-$column format.

$f(x)=\frac{(x+2)(x-3{)}^2}{e^x(x-1)\sqrt[\phantom{2}]{4x+7}}$