t^7+2t^6-24t^5=0

Solution for t^7+2t^6-24t^5=0 equation:

Simplifying
t7 + 2t6 + -24t5 = 0

Reorder the terms:
-24t5 + 2t6 + t7 = 0

Solving
-24t5 + 2t6 + t7 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't5'.
t5(-24 + 2t + t2) = 0

Factor a trinomial.
t5((-6 + -1t)(4 + -1t)) = 0

Subproblem 1
Set the factor 't5' equal to zero and attempt to solve:

Simplifying
t5 = 0

Solving
t5 = 0

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

Simplifying
t5 = 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 '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 3
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-6, 4}