Brackets can make a puzzle look complicated, but they also tell you where to split it. Treat each bracket as a single temporary quantity. Solve for that quantity before deciding which digits go inside.
Undo the last operation first
In (_ + _) × _ + 7 = 97, the last operation is adding seven. Subtract seven from the target to obtain (a + b)c = 90. Let S = a + b. You now need Sc = 90.
Two keypad digits can add to at most eighteen, while the outside digit c can be at most nine. Among the factors of ninety, only c = 5, 6 or 9 gives a possible sum. Those cases require sums of eighteen, fifteen and ten respectively.
Expand each case systematically
A sum of eighteen has only 9 + 9. A sum of fifteen has 6 + 9 and 7 + 8. A sum of ten has 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5. These groups account for all eight solutions. The cases do not overlap because each fixes a different outside multiplier.
A difference behaves differently from a sum
A sum of two digits ranges from zero to eighteen. A positive difference ranges only from one to nine. In (_ − _) × (_ + _) = 117, the factors nine and thirteen fit in only one order: the difference must be nine. It cannot be thirteen. This forces the first bracket to 9 − 0.
Keep transformations reversible
Multiplying both sides by a known nonzero divisor is safe. If the divisor is an empty blank, first rule out zero. If you divide by an expression that might be zero, you could silently discard a valid case or introduce an invalid calculation.
Try a smaller version
For (_ + _) ÷ 3 = 4, what total do the two blanks need?
Show the reasoning
Multiply four by three to get twelve. The unordered digit pairs are 3 + 9, 4 + 8, 5 + 7 and 6 + 6. Each bracket is twelve and its division by three is exact.
The general routine is: remove fixed outside constants, factor the remaining target, apply the bracket bounds, then list the digit pairs. This produces a search you can explain and check.