6t^4(t^2+8t+15)=0

Solution for 6t^4(t^2+8t+15)=0 equation:

Simplifying
6t4(t2 + 8t + 15) = 0

Reorder the terms:
6t4(15 + 8t + t2) = 0
(15 * 6t4 + 8t * 6t4 + t2 * 6t4) = 0
(90t4 + 48t5 + 6t6) = 0

Solving
90t4 + 48t5 + 6t6 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t4'.
6t4(15 + 8t + t2) = 0

Factor a trinomial.
6t4((5 + t)(3 + t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 't4' equal to zero and attempt to solve:

Simplifying
t4 = 0

Solving
t4 = 0

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

Simplifying
t4 = 0

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 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 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 + t = 0 + -5

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

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

Simplifying
t = -5
Subproblem 3
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

Simplifying
t = -3
Solution
t = {-5, -3}