To factor the expression \(9t^2 - 90t - 99\), we can start by factoring out the greatest common factor (GCF) from all the terms.
The GCF of \(9t^2\), \(-90t\), and \(-99\) is \(9\).
So we can factor out \(9\):
\[ 9(t^2 - 10t - 11) \]
Next, we need to factor the quadratic expression \(t^2 - 10t - 11\). We will look for two numbers that multiply to \(-11\) (the constant term) and add up to \(-10\) (the coefficient of the linear term \(t\)).
The two numbers that satisfy these conditions are \(-11\) and \(1\) because:
\[ -11 \times 1 = -11 \quad \text{and} \quad -11 + 1 = -10 \]
Now we can write the quadratic expression as:
\[ (t - 11)(t + 1) \]
Thus, the complete factorization of \(9t^2 - 90t - 99\) is:
\[ 9(t - 11)(t + 1) \]
So, the final factored form is:
\[ \boxed{9(t - 11)(t + 1)} \]