I got my answer deleted for the question, Is there any advantage in launching spacecraft from a high latitude, or why was Plesetsk built so far north?
I spent quite some time researching this question and found an interesting demonstration on the same forum using Tsiolkovsky's Rocket equation. Although the demonstration isn't totally accurate because it does not take into consideration gravitational forces, it nonetheless gives an introductory mathematical explanation as to the advantages of launching from the equator when attempting to orbit a payload.
One of the user who deleted my answer, @PearsonArtPhoto, answered the question 3 years ago and made the erroneous comment that such launches give marginal advantages based on the assumption that the only gain is the earth's higher rotational speed at the equator. However, the payload gain can be quite important due to the exponential nature of the Rocket equation and therefore on the cost of launch.
A NASA study dating back to 1959, made a detailed calculation of the the cost reduction of launching a Saturn rocket from the equator as compared to Cape Canaveral and concluded that equatorial LEOs are 80% more expensive propellant-wise due to required orbital plane changes.
For GTO orbits, Sea Launch company estimated 18 to 25% payload increasing when launching from the equator.