How did the Missouri Compromise attempt to settle the issue of slavery?

The Missouri compromise solved the problem by admitting Missouri as a slave state and Maine as a free state. That allowed the number of free states and slave states to be equal.

(Also dividing the rest of the Louisiana Purchase into slave and free territory).

In the early 1800s, the most divisive issue in the United States of america wasslavery. Following the Revolution, most states this to the north of Maryland began programs of gradually outlawing slavery, and in the early decades of the 1800s the slave-holding states were primarily in the south!