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There is no PAIR of integers that can satisfy those conditions - however
-1 x -1 x -8 x -9 =72
-1 + -1 + -8 + -9 = -19
and if we are not restricted to integers we can solve the simultaneous equations
x·y = 72
x+y = -19
to get a solution...
x = -y - 19 = -(y+19)
so x·y = -(y+19)y = -y² - 19y = 72
which reduces to the quadratic equation
y² + 19 + 72 = 0
Solving this we get the roots as (-19 + √73)/2 and (-19 - √73)/2
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