value of $a$ for which $25^x+(a+2)5^x-(a+3)<0$for at least one real $x$ 
Find the values of $a$ for which the inequality is satisfied for $25^x+(a+2)5^x-(a+3)<0$
for at least one real value of $x$

$\bf{My\; Try::}$ We can write it as $a(5^x-1)<-\left[25^x+2\cdot 5^x-3\right]$
So $$a < -\left(\frac{25^x-5^x+3\cdot 5^x-3}{5^x-1}\right) = -\frac{(5^x+3)(5^x-1)}{5^x-1} = -(5^x+3)$$
Now how can i solve after that help required, Thanks

$$(5^x)^2+(a+2)5^x-(a+3)=(5^x+a+3)(5^x-1)<0$$
If $5^x-1>0,1<5^x<-(a+3)$ which is possible if $1<-(a+3)\iff a<-4$
If $5^x-1<0,-(a+3)<5^x<1$ which is possible if $1>-(a+3)\iff a>-4$
So, we need $a\ne4$
