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Solve $$3^{2x + 1} - 3^{x + 3} - 3^x + 3^2 = 0$$
Correct Answer: 0
PLACEHOLDER ANSWER - the equation has two solutions. Put $$t = 3^x > 0$$; the equation becomes $$3t^2 - 27t - t + 9 = 0$$, i.e. $$3t^2 - 28t + 9 = 0$$, so $$(3t - 1)(t - 9) = 0$$. Then $$t = 9$$ or $$t = \frac{1}{3}$$, giving $$x = 2$$ or $$x = -1$$.
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