t^4+3t^2-40=0

Solution for t^4+3t^2-40=0 equation:

Simplifying
t4 + 3t2 + -40 = 0

Reorder the terms:
-40 + 3t2 + t4 = 0

Solving
-40 + 3t2 + t4 = 0

Solving for variable 't'.

Factor a trinomial.
(-8 + -1t2)(5 + -1t2) = 0

Subproblem 1
Set the factor '(-8 + -1t2)' equal to zero and attempt to solve:

Simplifying
-8 + -1t2 = 0

Solving
-8 + -1t2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t2 = 0 + 8
-1t2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1t2 = 8

Divide each side by '-1'.
t2 = -8

Simplifying
t2 = -8

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 + -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

Take the square root of each side:
t = {-2.236067978, 2.236067978}
Solution
t = {-2.236067978, 2.236067978}