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Product of negative integers

I am trying to find $x,y,z$ and $w$ such that $$x+y+z+w=x^2-xy+xz+yz+zw-wx-wy-wz-wx^2+wx^2$$
Is there any way to simplify this equation?

A:

Since we are looking for a solution where $x,y,z,w$ are positive, we are only looking for integer values of $x,y,z,w$. The equation becomes
$$(x+y+z+w)^2-(x+y+z+w)+(x^2-xy+xz+yz+zw-wx-wy-wz-wx^2)=0$$
which results in
$$(x+y+z+w)(x+y+z+w)-(x+y+z+w)+\big
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