Composition of Dirac delta function with a function in two variables

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I have a Dirac delta function of two variables: $\delta(s-z_{1}(1-z_{1})-z_{2}(1-z_{2}))$ which I need to solve. I know how to solve when there is only one variable: $\delta(s-z(1-z))$, in which case I can write $\delta(g(z))=\sum_{i}\frac{\delta(z-z_{i})}{|g'(z_{i})|}$ where the sum extends over the roots of $g(z)$. I don't know how to do the same for the two-variable case. Any hints would be appreciated. Thanks in advance.