Solve $$$\frac{\left(\lambda - 1\right) \left(10 \lambda + 1\right) \left(20 \lambda^{2} - 10 \lambda + 1\right)}{200} = 0$$$ for $$$\lambda$$$

Solve the equation $$$\frac{\left(\lambda - 1\right) \left(10 \lambda + 1\right) \left(20 \lambda^{2} - 10 \lambda + 1\right)}{200} = 0$$$ for $$$\lambda$$$.

Real roots

$$$\lambda = - \frac{1}{10} = -0.1$$$A

$$$\lambda = 1$$$A

$$$\lambda = \frac{1}{4} - \frac{\sqrt{5}}{20}\approx 0.138196601125011$$$A

$$$\lambda = \frac{\sqrt{5} + 5}{20}\approx 0.361803398874989$$$A

Complex roots

It seems that there are no complex roots.