Solve the equation : $x^2 − 6 |x − 2| − 28 = 0$

Solve the equation : $x^2 − 6 |x − 2| − 28 = 0$

The following is an absolute value quadratic equation that I want to
solve: $$x^2 − 6 |x − 2| − 28 = 0$$ Here is what I did :
$x^2 − 6 |x − 2| − 28 = 0$
$x^2 − 6 |x − 2| − 28 = 0$
$-6|x-2|=28-x^2$
$6|x-2|=x^2-28$
$6x-12=x^2-28$ or $28-x^2$ (Is this step correct ?)
Solving this two quadratic equations I get the answers $x=-2,8,-10,4$
But when I actually substitute these in the original equation I see that
only $x=8,-10 $ satisfy and other two solutions are invalid . Why so?