0=t^4-6t^2+5

Solution for 0=t^4-6t^2+5 equation:

Simplifying
0 = t4 + -6t2 + 5

Reorder the terms:
0 = 5 + -6t2 + t4

Solving
0 = 5 + -6t2 + t4

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + 6t2 + -1t4 = 5 + -6t2 + t4 + -5 + 6t2 + -1t4

Reorder the terms:
-5 + 6t2 + -1t4 = 5 + -5 + -6t2 + 6t2 + t4 + -1t4

Combine like terms: 5 + -5 = 0
-5 + 6t2 + -1t4 = 0 + -6t2 + 6t2 + t4 + -1t4
-5 + 6t2 + -1t4 = -6t2 + 6t2 + t4 + -1t4

Combine like terms: -6t2 + 6t2 = 0
-5 + 6t2 + -1t4 = 0 + t4 + -1t4
-5 + 6t2 + -1t4 = t4 + -1t4

Combine like terms: t4 + -1t4 = 0
-5 + 6t2 + -1t4 = 0

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

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

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

Simplifying
-5 + t2 = 0

Solving
-5 + t2 = 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 + t2 = 0 + 5

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

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

Simplifying
t2 = 5

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

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
Solution
t = {-2.236067978, 2.236067978, -1, 1}