Solving f((2x-1)/2)=x^2-x, a Functional Equation

Picked one by one from a mixed channel; title passed two strict editor passes and the clickbait rules.

A 6-minute video from SyberMath: “Solving f((2x-1)/2)=x^2-x, a Functional Equation”.

Video by SyberMath, played through YouTube's embedded player.