6t^8-12t^7-18t^6=0

Solution for 6t^8-12t^7-18t^6=0 equation:

Simplifying
6t8 + -12t7 + -18t6 = 0

Reorder the terms:
-18t6 + -12t7 + 6t8 = 0

Solving
-18t6 + -12t7 + 6t8 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t6'.
6t6(-3 + -2t + t2) = 0

Factor a trinomial.
6t6((-1 + -1t)(3 + -1t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 't6' equal to zero and attempt to solve:

Simplifying
t6 = 0

Solving
t6 = 0

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

Simplifying
t6 = 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 '(-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
Subproblem 3
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-1, 3}