Solve the equation $3^{2y+1} - 3^{y+2} + 3 = 3^y$.

1. Use laws of indices to express the equation in terms of $3^y$

$3(3^{2y}) - 3^2(3^y) + 3 = 3^y$
$3(3^y)^2 - 9(3^y) + 3 = 3^y$

2. Use a substitution to form a quadratic equation

Let $u = 3^y$.
$3u^2 - 9u + 3 = u$
$3u^2 - 10u + 3 = 0$

3. Solve the quadratic equation for $u$

$(3u - 1)(u - 3) = 0$
$u = \frac{1}{3}$ or $u = 3$

4. Solve for $y$

Since $u = 3^y$:
$3^y = \frac{1}{3} = 3^{-1} \implies y = -1$
$3^y = 3 = 3^1 \implies y = 1$