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

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

Simplifying
t(9 + -6t2 + t4) = 0
(9 * t + -6t2 * t + t4 * t) = 0
(9t + -6t3 + t5) = 0

Solving
9t + -6t3 + t5 = 0

Solving for variable 't'.

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

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