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# Equation solving

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**Equation solving** is field of mathematics that is about finding the functions or values that will make an equation true. An equation says that two expressions are equal. These expressions contain one or more unknowns, which are usually called free variables.

There are a number of changes (transformations) that can be done to make it easier to find the solution. There are many kinds of equation, and some have no solution in the domain (field) where they are studied. Other kinds of equation cannot be solved exactly, and approximation needs to be used. Similarly, a system of equations may have no solutions, or an infinite number of solutions.

## Methods of solution

Methods for solving equations include:

- Brute force, trial and error, estimated guess: It is often possible to find a solution for equations where there are only a limited (usually small) number of possibilities. This is the case for some Diophantine equations.
- Elementary algebra can be used for some
*simple equations* - There are algorithms for solving Systems of linear equations. Very often, linear algebra can be used.
- There are formulas for solving polynomial equations up to degree four. Except for special cases, polynomial equations of a degree higher than four need to be approximated, or solved numerically.
- Taylor series and curve fitting can be used to approximate polynomials or other functions.