How to Factor Equations?

Equations in mathematics consist of constant terms and variables. Basically variables are unknown terms in an equation; we will calculate the value of variable and place it in the equation to maintain the equality of the equation. So basically we use an equation to get the value of variable. Now let us see how to factor equations.
In order to get the value of unknown variable we will follow many different approaches. Generally we use the factorizing approach for solving an equation.

In Factorization we will divide an equation in two or more small parts; every part is called a factor of equation. We will get one separate value of variable from every factor of equation. Let us take an example to better understand the method of solving an equation by factors.

Step 1: Quadratic equation is x² - 7x – 10 = 0. In this Quadratic Equation we will find the value of variable 'x' by factorization method.

Step 2: Now we will write this equation as x² – 5x – 2x + 10 = 0. This equation is subdivided in four terms. We will search the common terms from this equation as:

x(x - 5) -2 (x - 5) = 0,

(x – 5)(x - 2) = 0,

Step 3: We have two factors of given equation and these factors are (x - 5) and (x - 2).

Step 4: Place every factor equals to zero to get the value of variable 'x'.

When x - 5 = 0 then

x = 5,

And when x – 2 = 0 then

x = 2,

Step 5: So value of variable x = 2, 5.