I know what you mean,

games like this are good practice.

You have 9 single-digit "variables" though.

The best way is probably to start with the last line and write the factors of 27,

which are 9 and 3, so you'd begin with writing those possibilities down.

3(5+4), 3(6+3), 3(7+2), 3(8+1)

(1+2)(9).

You cannot use 3(6+3).

Your last line must be one of the remaining 4.

You could pick one and then see if you can write the first 2 lines using the remaining 6 digits.

You find, the remaining 6 digits only combine correctly if you choose 3(8+1).

It's quite easy to start out by choosing digits in "add" and "multiply" combinations

and writing down the answers, but working backwards to discover the numbers chosen requires

some detective work.

In the solution as Denis gave, imagine combining the verticals in different combinations

of add and multiply.

You have horizontal answers, you could be given vertical ones instead.