0=-5t^2+20t+60

Solution for 0=-5t^2+20t+60 equation:

Simplifying
0 = -5t2 + 20t + 60

Reorder the terms:
0 = 60 + 20t + -5t2

Solving
0 = 60 + 20t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -60 = -60
-60 + -20t + 5t2 = 60 + 20t + -5t2 + -60 + -20t + 5t2

Reorder the terms:
-60 + -20t + 5t2 = 60 + -60 + 20t + -20t + -5t2 + 5t2

Combine like terms: 60 + -60 = 0
-60 + -20t + 5t2 = 0 + 20t + -20t + -5t2 + 5t2
-60 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2

Combine like terms: 20t + -20t = 0
-60 + -20t + 5t2 = 0 + -5t2 + 5t2
-60 + -20t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-60 + -20t + 5t2 = 0

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

Factor a trinomial.
5((-2 + -1t)(6 + -1t)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve:

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-2, 6}