9t=-2t^3-9t^2

Solution for 9t=-2t^3-9t^2 equation:

Simplifying
9t = -2t3 + -9t2

Reorder the terms:
9t = -9t2 + -2t3

Solving
9t = -9t2 + -2t3

Solving for variable 't'.

Reorder the terms:
9t + 9t2 + 2t3 = -9t2 + 9t2 + -2t3 + 2t3

Combine like terms: -9t2 + 9t2 = 0
9t + 9t2 + 2t3 = 0 + -2t3 + 2t3
9t + 9t2 + 2t3 = -2t3 + 2t3

Combine like terms: -2t3 + 2t3 = 0
9t + 9t2 + 2t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(9 + 9t + 2t2) = 0

Factor a trinomial.
t((3 + t)(3 + 2t)) = 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 + 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
Subproblem 3
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {0, -3, -1.5}