$a)$
$2(x-5) - x ( x+ 1) = x ( 5-x)$
$⇔2x-10-x^{2}-x=5x-x^{2}$
$⇔2x-x-5x-x^{2}+x^{2}=10$
$⇔-4x^{}=10$
$⇔x=\frac{-5}{2}$
$Vậy$ $x=\frac{-5}{2}$
$b)$
$x(x-5)-(x+2) (x-3)=6$
$⇔x^{2}-5x-x^{2}+3x-2x+6=6$
$⇔-4x^{}=0$
$x=0$
$Vậy$ $x=0$
$c)$
$(2x+1)(x-3)=2x (x+5)-4x$
$⇔2x^{2}-6x+x-3=2x^{2}+10x-4x$
$⇔2x^{2}-6x+x-2x^{2}-10x+4x=3$
$⇔-11x=3$
$⇔x= \frac{-3}{11} $
$Vậy$ $x= \frac{-3}{11} $
$d)$
$(x-5)(x+1) - ( x-2)(x+3)$
$=x^{2}+x-5x-5-x^{2}+2x-3x+6$
$=-5x+1^{}$