Complex sentence: Labor Party, Baker and other LGBT delegates persuaded the Convention to include in the party platform a plank supporting equal marriage rights for all adults, the first support for gay marriage by a major United States political party.
Split into simpler sentences: Labor Party, Baker and other LGBT delegates persuaded the Convention to include in the party platform a plank supporting equal marriage rights for all adults. This is believed to be the first support for gay marriage by any major United States political party.