Question
$$-8r^5+5r^4+9r^3+9r^2 = 0$$
Answer
$$ r = 0 $$
Explanation
In order to solve $ \color{blue}{ -8x^{5}+5x^{4}+9x^{3}+9x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ -8x^{5}+5x^{4}+9x^{3}+9x^{2} = x^2 \left( -8x^{3}+5x^{2}+9x+9 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ -8x^{3}+5x^{2}+9x+9 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Polynomial Equations Solver