Need help

First, let's simplify the right hand side of the equation a little bit. 

We get that $-9t+12-4t+23+4t^2-1=-13t+4t^2+34$

Now, we simply move all terms to one side. Note that most terms cancel out. 

we get the equation

$13t-34\le \:0$

Solving for t, we get

$13t\le \:34\\t\le \:\frac{34}{13}$

In interval notation, this is

$(-inf, \frac{34}{13}]$

Thanks! :)