# Solving quadratic equations by factorization

**Quadratic equations**

The general form of a quadratic equation is:

*a²* + b*x* – c = 0 (*a*, *b* and *c* are constants, and *a* ≠ 0)

The following equation is an example of a quadratic equation:

*x*(*x* + 4) = 45

However, if the brackets are multiplied out, it is easier to work out:

*x²* + 4*x* = 45

Quadratic equations has the rule where all the terms are on the right hand side. Therefore taking this a step further the equation becomes:

*x²* + 4*x* – 45 = 0

Quadratic equations can be solved by factorising the expression on the left hand side as shown in the following section:

**Solving quadratic equations by factorization**

The following equation is to be solved using the factorisation technique:

*x²* – 3*x* = 0 (rearrange so the terms are on the left hand side)

*x(x* – 3*)* = 0 (factorise the equation)

Therefore:

*x* = 0

or

*x* = 3