0=t(t^4-6t^2+9)

Solution for 0=t(t^4-6t^2+9) equation:

Simplifying
0 = t(t4 + -6t2 + 9)

Reorder the terms:
0 = t(9 + -6t2 + t4)
0 = (9 * t + -6t2 * t + t4 * t)
0 = (9t + -6t3 + t5)

Solving
0 = 9t + -6t3 + t5

Solving for variable 't'.
Remove the zero:
-9t + 6t3 + -1t5 = 9t + -6t3 + t5 + -9t + 6t3 + -1t5

Reorder the terms:
-9t + 6t3 + -1t5 = 9t + -9t + -6t3 + 6t3 + t5 + -1t5

Combine like terms: 9t + -9t = 0
-9t + 6t3 + -1t5 = 0 + -6t3 + 6t3 + t5 + -1t5
-9t + 6t3 + -1t5 = -6t3 + 6t3 + t5 + -1t5

Combine like terms: -6t3 + 6t3 = 0
-9t + 6t3 + -1t5 = 0 + t5 + -1t5
-9t + 6t3 + -1t5 = t5 + -1t5

Combine like terms: t5 + -1t5 = 0
-9t + 6t3 + -1t5 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-9 + 6t2 + -1t4) = 0

Factor a trinomial.
t((-3 + t2)(3 + -1t2)) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-3 + t2)' equal to zero and attempt to solve:

Simplifying
-3 + t2 = 0

Solving
-3 + t2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + t2 = 0 + 3
t2 = 0 + 3

Combine like terms: 0 + 3 = 3
t2 = 3

Simplifying
t2 = 3

Take the square root of each side:
t = {-1.732050808, 1.732050808}
Subproblem 3
Set the factor '(3 + -1t2)' equal to zero and attempt to solve:

Simplifying
3 + -1t2 = 0

Solving
3 + -1t2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t2 = 0 + -3
-1t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1t2 = -3

Divide each side by '-1'.
t2 = 3

Simplifying
t2 = 3

Take the square root of each side:
t = {-1.732050808, 1.732050808}
Solution
t = {0, -1.732050808, 1.732050808, -1.732050808, 1.732050808}