Let 푆 be a commutative semigroup, 퐾 a quadratically closed commutative field of characteristic different from 2, 퐺 a 2-cancellative abelian group and 퐻 an abelian group uniquely divisible by 2. The goal of this paper is to find the general non-zero solution f : S 2 → K of the d'Alembert type equation f (x + y , z + w) + f (x + σ (y) , z + τ (w) ) = 2 f (x , z) f (y , w) , x , y , z , w ∈ S , the general non-zero solution f : S 2 → G of the Jensen type equation f (x + y , z + w) + f (x + σ (y) , z + τ (w) ) = 2 f (x , z) , x , y , z , w ∈ S , the general non-zero solution f : S 2 → H of the quadratic type equation f (x + y , z + w) + f (x + σ (y) , z + τ (w) ) = 2 f (x , z) + 2 f (y , w) , x , y , z , w ∈ S , where σ , τ : S → S are two involutions. [ABSTRACT FROM AUTHOR]