Real root of $x(x+t)^2-4=0$ $\ge$ greatest real root of $4x^6-6x^4+4t^3x^3+t^6-3t^4=0$

Question

I have a problem that I can not solve although I know that the statement is true.

For all $t\ge0$ the real root of $x(x+t)^2-4=0$ is greater than or equal to the largest real root of $4x^6-6x^4+4t^3x^3+t^6-3t^4=0$. Does anyone have some idea to solve this problem?