verb (used with object), equalized, equalizing.
to make equal: to equalize tax burdens.
to make uniform: to equalize a rate of production.
Also, especially British, equalise.

1580–90; equal + -ize

equalization, noun
nonequalization, noun
nonequalized, adjective
nonequalizing, adjective
unequalize, verb (used with object), unequalized, unequalizing.
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
equalize or equalise (ˈiːkwəˌlaɪz)
1.  (tr) to make equal or uniform; regularize
2.  (intr) (in sports) to reach the same score as one's opponent or opponents
equalise or equalise
equali'zation or equalise
equali'sation or equalise

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

1590s, from equal + -ize. Related: Equalized; equalizing. Equalizer is from 1792; in the U.S. underworld slang sense of pistol, it is from c.1900.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Now they want to come up with some law or whatever to equalize grant
Scientists call this phenomenon osmosis, which tends to equalize the salinity
  of the two solutions.
The popping noise you hear can help equalize the pressure inside your ear.
Don't build complex systems that put government in the position of trying to
  equalize all resources or ban all contributions.
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