# Solve non-linear equation in R

I need to solve the following equation for $$x$$ in [0, 1]. Assume $$0<\alpha<1$$ and $$0<\lambda$$.

$$(1 - x)^{\alpha+1} - \lambda (x+1)^{\alpha+1} = -2\lambda (\alpha + 1) x^\alpha$$

Would very much appreciate any kind of help!