View the biography of Al-Khwarizmi

That fondness for science, ... that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala , confining it to what is easiest and most useful in arithmetic.

al-jabr means "restoring", referring to the process of moving a subtracted quantity to the other side of an equation.
al-muqabala is "comparing" and refers to subtracting equal quantities from both sides of an equation.
The Arabs contributed nothing new to the theory, but al-Khowirizmi (c. 825) states the usual rules, and the same is true of his successors.
David Eugene Smith. History of Mathematics (1923)