Solve the following equation for $x$ : $ \quad3^{2x+1}-10\cdot 3^x+3=0 $
I am baffled to solve this equation. With graphing I have found the answers to be x=1 and x=-1. I would like to know how to solve this equation though.
I have tried many different approaches including rearranging to these various forms (in no particular order):
$$3^{2x+1} - 3^{x+2} - 3^x + 3 = 0$$ $$ 3^{2x+1}\cdot(1-10\cdot 3^{-x-1}+3^{-2x}) = 0 $$ $$ -2x = 10\cdot 3^{-x-1}-3^0 $$
This equation has a term eliminated in it already.
The last equation written is the closest I have gotten to finding the answer, but I don't know how to proceed any further.
Hint: Substitute $y = 3^x$, you will get the quadratic equation $3y^2-10y+3=0$.