120=-16t^2+68t+60

Solution for 120=-16t^2+68t+60 equation:

Simplifying
120 = -16t2 + 68t + 60

Reorder the terms:
120 = 60 + 68t + -16t2

Solving
120 = 60 + 68t + -16t2

Solving for variable 't'.

Combine like terms: 120 + -60 = 60
60 + -68t + 16t2 = 60 + 68t + -16t2 + -60 + -68t + 16t2

Reorder the terms:
60 + -68t + 16t2 = 60 + -60 + 68t + -68t + -16t2 + 16t2

Combine like terms: 60 + -60 = 0
60 + -68t + 16t2 = 0 + 68t + -68t + -16t2 + 16t2
60 + -68t + 16t2 = 68t + -68t + -16t2 + 16t2

Combine like terms: 68t + -68t = 0
60 + -68t + 16t2 = 0 + -16t2 + 16t2
60 + -68t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
60 + -68t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -17t + 4t2) = 0

Factor a trinomial.
4((5 + -4t)(3 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -4t)' equal to zero and attempt to solve:

Simplifying
5 + -4t = 0

Solving
5 + -4t = 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 + -4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4t = 0 + -5
-4t = 0 + -5

Combine like terms: 0 + -5 = -5
-4t = -5

Divide each side by '-4'.
t = 1.25

Simplifying
t = 1.25
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 = {1.25, 3}