To solve this inequality, we need to simplify the left side first:

3^(x+2) - 2*3^(x+1) + 3^x < 12

Rewrite each term in terms of 3^x:

3^(x+2) = 3^x 3^2 = 93^x
23^(x+1) = 233^x = 63^x

Now substitute these back into the original inequality:

93^x - 63^x + 3^x < 12

Combine like terms:

(9 - 6 + 1)*3^x < 12

4*3^x < 12

Divide both sides by 4:

3^x < 3

Since 3 = 3^1, we have:

x < 1

Therefore, the solution to the inequality 3^(x+2) - 2*3^(x+1) + 3^x < 12 is x < 1.