We have de-soldered all flawed capacitors from the motherboard and can now install our replacements. Watch the capacitors' polarity. If you confuse plus with minus, the capacitor will explode and you will have put in a lot of hard work for nothing. New capacitors come with a longer-legged plus pole. To make sure you get things right, take a close look at the capacitor. It is clearly labeled, e.g. with numerous "minus" symbols and an arrow pointing at the associated leg. Both poles are also clearly tagged on your motherboard.
Watch the polarity when replacing the capacitors on a motherboard.
Moving the capacitor all the way down
Slightly bend anode and cathode (legs) to the side, so the capacitors won't fall out after placing them on the motherboard.
Soldering the capacitors...
...and pruning left-over material.