Question

5*​15^​(x)-​3*​5^​(x+​1)-​3^(​x)+​3

Answer 1

$5*15^x-3*5^{x+1}-3^x+3=0\\\\ 5*(5*3)^x-3*5^{x+1}-3^x+3=0\\\\ 5*5^x*3^x-3*5^{x+1}-3^x+3=0\\\\ 5^{x+1}*3^x-5^{x+1}*3-(3^x-3)=0\\\\ 5^{x+1}*(3^x-3)-(3^x-3)=0\\\\ (5^{x+1}-1)*(3^x-3)=0\\\\ 5^{x+1}-1=0\ \ OR\ \ 3^x-3=0\\\\ 5^{x+1}=1\ \ OR\ \ 3^x=3\\\\ 5^{x+1}=5^0\ \ OR\ \ 3^x=3^1\\\\ x+1=0\ \ OR\ \ x=1\\\\ x=-1\ \ OR\ \ x=1$

Ответ: $\{-1;\ 1\}$