$a)(x+3)^2-(x-4)(x+8)=1$
$⇔x^2+6x+9-(x^2+4x-32)=1$
$⇔x^2-x^2+6x-4x+9+32=1$
$⇔2x=-40$
$⇔x=-20$
Vậy $S=\{-20\}$
$b)(x+3)(x^2-3x+9)-x(x-2)(x+2)=15$
$⇔x^3+27-x(x^2-4)=15$
$⇔x^3-x^3+27+4x=15$
$⇔4x=-12$
$⇔x=-3$
Vậy $S=\{-3\}$
$c)(x-2)^2-(x+3)^2-4(x+1)=5$
$⇔x^2-4x+4-x^2-6x-9-4x-4=5$
$⇔-14x=14$
$⇔x=-1$
Vậy $S=\{-1\}$
$d)(2x-3)(2x+3)-(x-1)^2-3x(x-5)=-44$
$⇔4x^2-9-x^2+2x-1-3x^2+15x=-44$
$⇔17x=-34$
$⇔x=-2$
Vậy $S=\{-2\}$
$e)(x-2)^3-(x-3)(x^2+3x+9)+6(x+1)^2=49$
$⇔x^3-6x^2+12x-8-x^3+27+6x^2+12x+6=49$
$⇔24x=24$
$⇔x=1$
Vậy $S=\{1\}$
$f)5x(x-3)^2-5(x-1)^3+15(x-2)(x+2)=5$
$⇔5x(x^2-6x+9)-5(x^3-3x^2+3x-1)+15(x^2-4)=5$
$⇔5x^3-30x^2+45x-5x^3+15x^2-15x+5+15x^2-60=5$
$⇔30x=60$
$⇔x=2$
Vậy $S=\{2\}$
$g)(x+3)^3-x(3x+1)^2+(2x+1)(4x^2-2x+1)-3x^2=42$
$⇔x^3+9x^2+27x+27-x(9x^2+6x+1)+8x^3+1-3x^2=42$
$⇔x^3+9x^2+27x+27-9x^3-6x^2-x+8x^3+1-3x^2=42$
$⇔26x=14$
$⇔x=\dfrac{7}{13}$
Vậy $S=\{\dfrac{7}{13}\}$
