-9t^2-24t+9=0

Solution for -9t^2-24t+9=0 equation:

Simplifying
-9t2 + -24t + 9 = 0

Reorder the terms:
9 + -24t + -9t2 = 0

Solving
9 + -24t + -9t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -8t + -3t2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

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

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

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

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
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
Solution
t = {0.3333333333, -3}