If there is in a category $\mathcal{A}$ finite products and equalizers then it has pullbacks My homework consist in showing that "If there is in a category $\mathcal{A}$ finite coproducts and coequalizers then it has pushouts" based on the proof that "If there is in a category $\mathcal{A}$ finite products and equalizers then it has pullbacks" .This  last proof was given in class but somehow is lost in my notes, and I'm looking for it. If anyone of you can sketch it or give me any hint I'll be glad. Thank you in advance

Hint: Construct the pullback $A \times_C B$ as the equalizer of two morphisms $A \times B \to C$ (suitably defined). If you have no idea, recall the construction of pullbacks in $\mathsf{Set}$. The general case works verbatim.
