High School Algebra

In high school algebra, you all studied topics such as

• Techniques for manipulating various equations and expressions, including
  • finding common denominators and simplifying fractions, for example:

    

  • completing the square in quadratic expressions, for example:

    

  • rationalizing expressions with radicals, for example:

    

• Factoring polynomials, for instance:

  

• Expanding polynomials by "FOIL", the binomial theorem, etc.

Most of these techniques were probably introduced there as tools for problems requiring solving equations of various types. And in fact, algebra is often defined as the science or art of solving equations in one or more unknowns.