$$f^5-8f^4-7f^3 = 0$$
Answer
$$ \begin{matrix}f_1 = 0 & f_2 = 4-\sqrt{ 23 } & f_3 = 4+\sqrt{ 23 } \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ x^{5}-8x^{4}-7x^{3} = 0 } $, first we need to factor our $ x^3 $.
$$ x^{5}-8x^{4}-7x^{3} = x^3 \left( x^{2}-8x-7 \right) $$$ x = 0 $ is a root of multiplicity $ 3 $.
The remaining roots can be found by solving equation $ x^{2}-8x-7 = 0$.
$ x^{2}-8x-7 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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