$15x² + 17x + 4 =0$
$⇔15x²+5x+12x+4=0$
$⇔5x(3x+1)+4(3x+1)=0$
$⇔(3x+1)(5x+4)=0$
⇔\(\left[ \begin{array}{l}3x+1=0\\5x+4=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}3x=-1\\5x=-4\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-\frac{1}{3}\\x=-\frac{4}{5}\end{array} \right.\)