Question
$$15p^6-30p^5+15p^4-\frac{1}{5} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 15p^6-30p^5+15p^4-\frac{1}{5} &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot15p^6-5\cdot30p^5+5\cdot15p^4-5\cdot\frac{1}{5} &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]75p^6-150p^5+75p^4-1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver