t^4-11t^2+30=0

Solution for t^4-11t^2+30=0 equation:

Simplifying
t4 + -11t2 + 30 = 0

Reorder the terms:
30 + -11t2 + t4 = 0

Solving
30 + -11t2 + t4 = 0

Solving for variable 't'.

Factor a trinomial.
(5 + -1t2)(6 + -1t2) = 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

Take the square root of each side:
t = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(6 + -1t2)' equal to zero and attempt to solve:

Simplifying
6 + -1t2 = 0

Solving
6 + -1t2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t2 = 0 + -6
-1t2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1t2 = -6

Divide each side by '-1'.
t2 = 6

Simplifying
t2 = 6

Take the square root of each side:
t = {-2.449489743, 2.449489743}
Solution
t = {-2.236067978, 2.236067978, -2.449489743, 2.449489743}