-16t^2+96t+180=0

Solution for -16t^2+96t+180=0 equation:

Simplifying
-16t2 + 96t + 180 = 0

Reorder the terms:
180 + 96t + -16t2 = 0

Solving
180 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + 24t + -4t2) = 0

Factor a trinomial.
4((15 + -2t)(3 + 2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(15 + -2t)' equal to zero and attempt to solve:

Simplifying
15 + -2t = 0

Solving
15 + -2t = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2t = 0 + -15
-2t = 0 + -15

Combine like terms: 0 + -15 = -15
-2t = -15

Divide each side by '-2'.
t = 7.5

Simplifying
t = 7.5
Subproblem 2
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {7.5, -1.5}