Find the values of x when x^2-6=x

We need to factorise this equation to solve it.

The first step for factorisation is to make the equation equal to zero. We can do this by subtracting x from both sides to get:

x²-x-6=0

The coefficent in front of the x term is -1. We need to find two numbers that sum to -1 and mulitply together to make -6.

The two numbers that do this are -3 and 2. We use these in brackets as follows:

(x-3)(x+2)=0

Now to find the two possible values of x we need to solve the equation in each of the brackets individually. 

ie. solve x-3=0 and x+2=0

So our values for x are -2 and 3.