Hello there,
Let's solve it first so that we can understand whats going on in the equation
(x-4)²-10=15
add 10 to both sides
(x-4)²=25
square root both sides
(Okay, so here is where the problem can have 2 solutions. Because the square root of 25 could be (5*5) or it could be (-5*-5). If it's positive five then...
x-4=5
add 4 to both sides
x=9
if it's negative 5 then...
x-4=-5
add 4 to both sides
x=-1
So the answer could be x=-1 or x=9.
It has two solutions because there are two possibilities for the answer to the square root of 25.
I hope this help, and if you have any more questions, please feel free to ask me.
Have a nice day!