Insoluble means incapable of being dissolved. Unsolvable means impossible to solve. Less careful writers use these words interchangeably. However, the definitions of these two words make very clear that insoluble and unsolvable are not interchangeable.
Consider the example sentence in the cropped graphic above. By using insoluble, the writer communicates that the production problem is unable to dissolve in something. But problems don’t dissolve into anything; they don’t dissolve at all. Unsolvable is the better word choice.
Knowing when to use insoluble is not unsolvable. Understand the difference in definition, and you will know which word will more clearly communicate your meaning. That greater precision in language will increase the effectiveness of your writing. And that will in turn make a better presentation of both you and your brands to your audience.