The roots of polynomial $ p(y) $ are:
$$ \begin{aligned}y_1 &= 0.3452\\[1 em]y_2 &= -0.2942\\[1 em]y_3 &= 2.4745+1.9303i\\[1 em]y_4 &= 2.4745-1.9303i \end{aligned} $$Step 1:
Combine like terms:
$$ y^4-5y^3+ \color{blue}{6y^2} + \color{blue}{4y^2} -1 = y^4-5y^3+ \color{blue}{10y^2} -1 $$Step 2:
Polynomial $ y^4-5y^3+10y^2-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.