To solve the inequality, we can rewrite it as:

3(2^x)^2 + 2(3^x)^2 - 5(23)^x < 0

Let's make a substitution:

Let y = (2^x)^2

Now the inequality becomes:

3y + 23^(2log3(y)) - 5y^(log3(6)) < 0

Simplify the inequality further:

3y + 23^(2(xlog2(2))) - 5*y^(log3(6)) < 0

3y + 18 - 5*y^(log3(6)) < 0

Rewrite the inequality back in terms of x:

3(2^x)^2 + 18 - 5(2^x)^(log2(6)) < 0

Since 18 is a constant term, we can ignore it in terms of the inequality.

So, the final inequality is:

3(2^x)^2 - 5(2^x)^(log2(6)) < 0

This inequality can be further simplified by using some properties of logarithms, but it may not be possible to find an exact solution without using numerical methods.