Decolonization in Rhodesia was complicated. First, there was the Unilateral Declaration of Independence by Ian Smith's government in 1965. Then there was the civil war that followed it. After that came a peace agreement between the British, the Rhodesian government, and the black African rebels of two guerrilla armies affiliated with liberation movements: the Zimbabwe African National Union and the Zimbabwe African People's Union.
When the war finally ended in 1979, the British brokered the peace treaty that allowed for elections in which black and white Rhodesians could all vote for the first time. A black Rhodesian was elected prime minister, and as agreed, formal decolonization from Britain proceeded, and the country became independent in 1980 as Zimbabwe.
Why did decolonization happen this way in Rhodesia? There had been a period of unrest in the country, beginning after the end of the Second World War, by black nationalists anxious to end white minority rule and eventually end British colonialism. When Ian Smith became prime minister, he tried to forestall this by offering legal, political, social, and economic improvements to the lives of black Rhodesians, but he wouldn't consider changes to the country's constitution which would have made majority rule possible. The nationalists took their case to the British, citing majority rule and decolonization in India and Ghana, both former British colonies by the late 1950s. When the British pressured Smith to accommodate the nationalists, he responded by declaring independence, saying he would bring majority rule to Rhodesia on his own terms. Impatient nationalists started the civil war which eventually led to Rhodesia's emergence from British colonialism as Zimbabwe.
You should read Ian Smith's book on this subject, The Great Betrayal. It makes Smith's case personally, but it also gives you a good summary of the "white" side of the argument. For the "black" side of the argument, to read what it was like to live in Smith's Rhodesia and to understand the nationalist's side in the civil war, read Harvest of Thorns by Shimmer Chinodya. Both are excellent, and I highly recommend them.