Solve for x\displaystyle {x} :

 7x27x+12+4x29=6123x\displaystyle \frac{{7}}{{{x}^{{2}}-{7}{x}+{12}}}+\frac{{4}}{{{x}^{{2}}-{9}}}=\frac{{6}}{{{12}-{3}{x}}}    
 x=\displaystyle {x}=      
(type: "x=? is not applicable" if one of the solutions is not applicable)