(x-3)⁴-3(x-3)²-10=0

(x-3)⁴-3(x-3)²-10=0

To solve this equation, we can substitute a new variable. Let's denote (x-3) as t:

t⁴-3t²-10=0

Now, we have a quadratic equation in terms of t. We can solve it by factoring or using the quadratic formula.

(t²-5)(t²+2)=0

From this, we get two equations:

1. t²-5=0, which gives t=±√5.

2. t²+2=0, which has no real solutions.

Now, substitute back t=(x-3):

(x-3)²=±√5

To solve for x, take the square root of both sides:

x-3=±√(±√5)

Finally, solve for x:

x=3±√(±√5)