Explain how the federal government tried to resolve the issue of slavery in the western territories during the 1850s.

With the California Gold Rush, California's population increased dramatically, such that, as early as 1849, it was seeking admittance as a State into the Union. In the process, however, it awakened a controversy which would continue to shape the United States all the way into the Civil War.
Within its Constitution, California included provisions banning slavery. This would have aligned California with northern abolitionists on that issue. The result was to create dissension within the United States government surrounding California's admittance into the Union.
In short, there seems to have been three positions on the slavery question: southern slave-holders defined slavery as a right, and opposed all attempts to limit its spread into the territories. Meanwhile abolitionists perceived it as a moral outrage, and demanded that further spread of the institution be halted. Meanwhile, the Compromise of 1850 advanced a third view: that of popular sovereignty. Popular sovereignty held that the people living within the territories should determine for themselves on the legality or illegality of slavery.
Later, the Kansas-Nebraska Act would expand popular sovereignty to apply to the Kansas and Nebraska territories. The result, however, was to generate turmoil and sectarian violence, as both abolitionists and defendants of slavery moved into Kansas in order to influence the vote. With the Dred Scott decision, the Supreme Court would weigh in on this question, defining slavery in terms of property rights, and ruling that Congress had no authority to legislate against it in the territories. This ruling greatly angered northerners, further intensifying the divisions within the country.
Lincoln's victory in the 1860 election would be answered with secession, leading to the start of the Civil War.

As the United States was expanding due to the acquisition of land in the 1840s, the federal government attempted to deal with the growing issue regarding the spread of slavery. The federal government tried to resolve the issue regarding the spread of slavery in the 1850s. The first attempt was when the Compromise of 1850 was made. The Compromise of 1850 allowed for California to enter the Union as a free state and banned the trading of slaves in Washington, D.C. It also allowed the people to decide if slavery would exist in the Utah and New Mexico territories. The Fugitive Slave Act was passed, which required northerners to help capture runaway slaves and return them to their owners in the South.
In 1854, the Kansas-Nebraska Act was passed. This law created the Kansas and Nebraska territories. It allowed the people to decide if slavery would exist in these territories. This law effectively ended the Missouri Compromise. It contributed to fighting in Kansas regarding whether Kansas would or would not have slavery.
These attempts to resolve the issue dealing with the spread of slavery were not successful in preventing the start of the Civil War in 1861.

Slavery was a cruel and exploitative act of racial discrimination in the 18th century. The extension of slavery into the western territories caused an extensive debate, especially because the North and the South had stayed separate regarding trade, ideology, and social values. The federal government chose to compromise to resolve the issue of war temporarily. However, the compromises did not take long before they started to become one-sided. As a result, the already existing divide between the North and the South become more distinct. Political leaders were forced to deal with the issue of slave trade since the state had established a balance with an equal number of councils from both the free and the slave states.
When the extension of slavery reached Missouri, the balance would be affected which led to Henry Clay of Kentucky to momentarily resolve the matter by crafting a negotiation. The craft which is known in history as the Missouri compromise would bring the state to the Union of a slave state while Maine was converted as a free state to balance the situation. Equally, the agreement made future captivity illegal in Louisiana. The Clay compromise solved the immediate problem, but the case would not extend in future negotiations. For instance, when the United States entered into war with Mexico, the issue of slavery resurfaced. The then representative of Pennsylvania, David Wilmot, suggested that slavery should be prohibited in any territory the United States managed to acquire. While the northern politicians backed the act, the southern councils considered it unconstitutional. The Wilmot’s amendment never came to pass.

The end of the Mexican War was both a blessing and a curse for the United States.  The nation gained a great deal of new territory, but it could not decide whether or not this new land would be free or slave.  Initially, David Wilmot proposed that the new land should be entirely free; of course, this was considered a dead letter in Congress and Southerners voted against this.  There was also talk of extending the Compromise of 1820 dividing line between free and slave territory, but this would split California in half. 
The solution, the Compromise of 1850, came from Henry Clay.  It was an omnibus bill, which meant that it had to be passed as a whole unit.  The bill ensured that California would come in as a free state, New Mexico Territory could vote on whether or not to have slaves, the slave trade would be ended in Washington D.C., and the North would tighten the Fugitive Slave Law.  The bill passed, but it really made no one happy.  California was filled with miners and merchants, most of whom did not own slaves.  New Mexico was too dry to support cotton without extensive irrigation, and slave owners in Washington could go to neighboring Virginia or Maryland to buy their slaves.  The Fugitive Slave Law meant that more federal dollars would be used to bring fugitive slaves back to the South.  There were problems with this, as slave catchers were paid a bounty for each slave returned, and there were instances of some free men being sold into slavery.  
Another solution was Stephen Douglas's Kansas-Nebraska Act which allowed the people who lived in these territories the right to vote on whether or not they could own slaves.  Kansas was soon filled by abolitionists and pro-slavery advocates, and a state of war existed there starting in 1858 as both sides tried to intimidate and kill each other.