-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.
(25 + -1t2)(16 + t2) = 0

Factor a difference between two squares.
((5 + t)(5 + -1t))(16 + t2) = 0

Subproblem 1
Set the factor '(16 + t2)' equal to zero and attempt to solve:

Simplifying
16 + t2 = 0

Solving
16 + t2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + t2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + t2 = 0 + -16
t2 = 0 + -16

Combine like terms: 0 + -16 = -16
t2 = -16

Simplifying
t2 = -16

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}