Can anyone help me solve this? Thank you so so much!
16x^3 -48x^2 -9x + 27=0
By guessing one root...
My "guess" is x=3, now you should know how to continue.
Read here please: Rational Zeros of Polynomials
This cubic can be factored by grouping. Look at the first pair of terms and factor out the GCF; then do the same for the last pair.
$\displaystyle \begin{aligned}
16x^3 - 48x^2 - 9x + 27 &= 0 \\
16x^2(x - 3) - 9(x - 3) &= 0\\
(x - 3)(16x^2 -9) &= 0
\end{aligned}
$
Can you take it from here? Finish factoring (look at 16x^2 - 9), and set each factor equal to 0.