$\mathbb{R}$ is used to represent the set of all real numbers and $t$ is a given invariant real number,$t≠0$，Find all functions that satisfiesf: $\mathbb{R} \to\mathbb{R}\, \forall x,y \in\mathbb{R}$ (independent transformation between $x$ and $y$)$ f\left( x\cdot f\left( y \right) +t \right) =f\left( x\cdot y^2 \right) -\left( 1-2tx+x^2+f\left( x \right) \right) \cdot f\left( y \right) -f\left( x \right) +t^2-1 $
I try to use special value methods when let $x=0$ or $y=0$ or $x=-y$ to simplify. But how to do next? Is there a universal method for this type of problem and recommend books？
