If 4x+5 is a factor of 12x^2-x+c, this means that
[tex]12x^2-x+c=(ax+b)(4x+5)=4ax^2+4bx+5ax+5b=4ax^2+(4b+5a)x+5b[/tex]
Where a and b are two constants.
Then, we can find the values of a and b as follows:
[tex]\begin{gathered} 12x^2=4ax^2 \\ \Rightarrow a=3 \\ -x=(4b+5a)x \\ \Rightarrow-1=(4b+5a)=4b+5\cdot3=4b+15 \\ \Rightarrow-16=4b \\ \Rightarrow b=-4 \end{gathered}[/tex]
Finally, we can find the value of c
[tex]\begin{gathered} c=5b \\ \Rightarrow c=5(-4)=-20 \\ \Rightarrow c=-20 \end{gathered}[/tex]
The answer is c=-20
