(x-1)(x²+8x+16)=6(x+4)

x²+8x+16=(x+4)²=(x+4)(x+4)

(x-1)(x²+8x+16)=6(x+4)
(x-1)(x+4)(x+4)-6(x+4)=0
(x+4)((x-1)(x+4)-6)=0

(x-1)(x+4)=x²-x+4x-4=x²+3x-4

(x+4)(x²+3x-4-6)=0
(x+4)(x²+3x-10)=0
$\left \{ {{x+4=0} \atop { x^{2} +3x-10=0}} \right. \\ \left \{ {{x=-4} \atop { x^{2} +3x-10=0}} \right. \\$

x² +3x-10=0
D=3²-4*(-10)*1=9+0=49=7²
$x_{1}= \frac{-3- \sqrt{49} }{2*1} = \frac{-3-7}{2} = \frac{-10}{2}=-5 \\ x_{2}= \frac{-3+ \sqrt{49} }{2*1} = \frac{-3+7}{2} = \frac{4}{2}=2$

$\left \{ {{x=-4}\atop { x=2}} \atop { x=-5}}\right. \\$