-t^4-9t^2+400=0

Solution for -t^4-9t^2+400=0 equation:

Simplifying
-1t4 + -9t2 + 400 = 0

Reorder the terms:
400 + -9t2 + -1t4 = 0

Solving
400 + -9t2 + -1t4 = 0

Solving for variable 't'.

Factor a trinomial.
(16 + -1t2)(25 + t2) = 0

Factor a difference between two squares.
((4 + t)(4 + -1t))(25 + t2) = 0

Subproblem 1
Set the factor '(25 + t2)' equal to zero and attempt to solve:

Simplifying
25 + t2 = 0

Solving
25 + t2 = 0

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

Add '-25' to each side of the equation.
25 + -25 + t2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + t2 = 0 + -25
t2 = 0 + -25

Combine like terms: 0 + -25 = -25
t2 = -25

Simplifying
t2 = -25

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 '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Subproblem 3
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-4, 4}