-3t^2+30t-72=0

Solution for -3t^2+30t-72=0 equation:

Simplifying
-3t2 + 30t + -72 = 0

Reorder the terms:
-72 + 30t + -3t2 = 0

Solving
-72 + 30t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 10t + -1t2) = 0

Factor a trinomial.
3((-6 + t)(4 + -1t)) = 0

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

Simplifying
-6 + t = 0

Solving
-6 + t = 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 + t = 0 + 6

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

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

Simplifying
t = 6
Subproblem 2
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}