-16t^2+144t-180=0

Solution for -16t^2+144t-180=0 equation:

Simplifying
-16t2 + 144t + -180 = 0

Reorder the terms:
-180 + 144t + -16t2 = 0

Solving
-180 + 144t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 36t + -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}