Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set - Page 304: 66

$(x-9)(4x-3)$

The two numbers whose product is $ac= 4(27)=108 $ and whose sum is $b= -39 $ are $\{ -36,-3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 4x^2-39x+27 $, is \begin{array}{l}\require{cancel} 4x^2-36x-3x+27 \\\\= (4x^2-36x)-(3x-27) \\\\= 4x(x-9)-3(x-9) \\\\= (x-9)(4x-3) .\end{array}