t^4-20*t^2-125=0

Solution for t^4-20*t^2-125=0 equation:

Simplifying
t4 + -20t2 + -125 = 0

Reorder the terms:
-125 + -20t2 + t4 = 0

Solving
-125 + -20t2 + t4 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -1t2)(25 + -1t2) = 0

Factor a difference between two squares.
(-5 + -1t2)((5 + t)(5 + -1t)) = 0

Subproblem 1
Set the factor '(-5 + -1t2)' equal to zero and attempt to solve:

Simplifying
-5 + -1t2 = 0

Solving
-5 + -1t2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t2 = 0 + 5
-1t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1t2 = 5

Divide each side by '-1'.
t2 = -5

Simplifying
t2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 0

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

Add '-5' to each side of the equation.
5 + -5 + t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + t = 0 + -5
t = 0 + -5

Combine like terms: 0 + -5 = -5
t = -5

Simplifying
t = -5
Subproblem 3
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-5, 5}