-12t^2+48t+60=0

Solution for -12t^2+48t+60=0 equation:

Simplifying
-12t2 + 48t + 60 = 0

Reorder the terms:
60 + 48t + -12t2 = 0

Solving
60 + 48t + -12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '12'.
12(5 + 4t + -1t2) = 0

Factor a trinomial.
12((5 + -1t)(1 + t)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Solution
t = {5, -1}