To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, we perform the multiplication and division from left to right:
36.(-57) = -2052
69.(-37) = -2553

Now, we substitute these values back into the expression:
105.57 + (-2052)/(-2553) - 69

Next, we simplify the division:
(-2052)/(-2553) = 0.803

Now, we substitute this value back into the expression:
105.57 + 0.803 - 69

Finally, we perform the addition and subtraction from left to right:
105.57 + 0.803 = 106.373
106.373 - 69 = 37.373

Therefore, the solution to the expression 105.57 + 36.(-57)/69.(-37) - 69 is 37.373.