-3t^2+24t-45=0

Solution for -3t^2+24t-45=0 equation:

Simplifying
-3t2 + 24t + -45 = 0

Reorder the terms:
-45 + 24t + -3t2 = 0

Solving
-45 + 24t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 8t + -1t2) = 0

Factor a trinomial.
3((-5 + t)(3 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
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 2
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 = {5, 3}