How did you get x=2, x=-6 and x=-4

The problem

There is another way around to solve this equation.

Multiply both sides of the bellow equation by (x + 4)(x - 4)

You will have the following equation to solve:

x(x - 4) = 2(x^2 - 6)

........

........

x1 = 2

x2 = -6

Lets double check, plug x = 2 into

Indeed, x = 2 is one solution.

Plug x = -6 into the equation

Indeed, x = -6 is a second solution.