s^4-2s^2t^2+t^4=0

Solution for s^4-2s^2t^2+t^4=0 equation:

Simplifying
s4 + -2s2t2 + t4 = 0

Reorder the terms:
-2s2t2 + s4 + t4 = 0

Solving
-2s2t2 + s4 + t4 = 0

Solving for variable 's'.

Factor a trinomial.
(s2 + -1t2)(s2 + -1t2) = 0

Factor a difference between two squares.
((s + t)(s + -1t))(s2 + -1t2) = 0

Factor a difference between two squares.
((s + t)(s + -1t))(s + t)(s + -1t) = 0

Subproblem 1
Set the factor '(s + t)' equal to zero and attempt to solve:

Simplifying
s + t = 0

Solving
s + t = 0

Move all terms containing s to the left, all other terms to the right.

Add '-1t' to each side of the equation.
s + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
s + 0 = 0 + -1t
s = 0 + -1t
Remove the zero:
s = -1t

Simplifying
s = -1t
Subproblem 2
Set the factor '(s + -1t)' equal to zero and attempt to solve:

Simplifying
s + -1t = 0

Solving
s + -1t = 0

Move all terms containing s to the left, all other terms to the right.

Add 't' to each side of the equation.
s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
s + 0 = 0 + t
s = 0 + t
Remove the zero:
s = t

Simplifying
s = t
Subproblem 3
Set the factor '(s + t)' equal to zero and attempt to solve:

Simplifying
s + t = 0

Solving
s + t = 0

Move all terms containing s to the left, all other terms to the right.

Add '-1t' to each side of the equation.
s + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
s + 0 = 0 + -1t
s = 0 + -1t
Remove the zero:
s = -1t

Simplifying
s = -1t
Subproblem 4
Set the factor '(s + -1t)' equal to zero and attempt to solve:

Simplifying
s + -1t = 0

Solving
s + -1t = 0

Move all terms containing s to the left, all other terms to the right.

Add 't' to each side of the equation.
s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
s + 0 = 0 + t
s = 0 + t
Remove the zero:
s = t

Simplifying
s = t
Solution
s = {-1t, t, -1t, t}