Addition Distributes over Multiplication?

We know that by the distributive property \(a(b+c) = ab + ac\) is an identity. However, \(a + bc = (a+b)(a+c) \) is not an identity.

Find the number of ordered triples of integers \((a,b,c) \) in the interval \([-10,10] \) such that \(a+bc = (a+b)(a+c) \).

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