a: (2x+5)(12-3x)>0
=>\(\left(2x+5\right)\left(3x-12\right)< 0\)
=>(2x+5)(x-4)<0
TH1: \(\left\{{}\begin{matrix}2x+5>0\\x-4< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>-\dfrac{5}{2}\\x< 4\end{matrix}\right.\)
=>\(-\dfrac{5}{2}< x< 4\)
TH2: \(\left\{{}\begin{matrix}2x+5< 0\\x-4>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< -\dfrac{5}{2}\\x>4\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
b: 2xy-4x=y+7
=>2x(y-2)-(y+7)=0
=>2x(y-2)-(y-2+9)=0
=>2x(y-2)-(y-2)=9
=>(y-2)(2x-1)=9
=>\(\left(2x-1;y-2\right)\in\left\{\left(1;9\right);\left(9;1\right);\left(-1;-9\right);\left(-9;-1\right);\left(3;3\right);\left(-3;-3\right)\right\}\)
=>\(\left(2x;y\right)\in\left\{\left(2;11\right);\left(10;3\right);\left(0;-7\right);\left(-8;1\right);\left(4;5\right);\left(-2;-1\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(1;11\right);\left(5;3\right);\left(0;-7\right);\left(-4;1\right);\left(2;5\right);\left(-1;-1\right)\right\}\)