Taking the LCM of the right hand side of the equation, we have
4(2x−3)−2(x+5)(x+5)(2x−3)=6x+m2x2+7x−15\frac{4(2x-3)-2(x+5)}{(x+5)(2x-3)} = \frac{6x+m}{2x^{2}+7x-15}(x+5)(2x−3)4(2x−3)−2(x+5)=2x2+7x−156x+m
Comparing the numerators, we have
4(2x−3)−2(x+5)=6x+m4(2x-3) - 2(x+5) = 6x+m4(2x−3)−2(x+5)=6x+m
8x−12−2x−10=6x−22=6x+m8x-12-2x-10 = 6x-22 = 6x+m8x−12−2x−10=6x−22=6x+m
⇒m=−22\Rightarrow m = -22⇒m=−22
