The South agreed with adding no federal restrictions on slavery that would be placed in Utah or New Mexico. However, slavery was still maintained in the nations capital. But slave trade was still tolerated. This eventually led to the Fugitive Slave Law to be passed.
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Even though each side received benefits, it was the Northern states that gained more advantage, it seemed. The balance of the Senate now became with the free states and the major victory for the South was the Fugitive Law
Unfortunately, the Northerners claimed the law was unfair in which the violation of the fugitive slave law created a bigger issue in time..