72=-16t^2+108t

Solution for 72=-16t^2+108t equation:

Simplifying
72 = -16t2 + 108t

Reorder the terms:
72 = 108t + -16t2

Solving
72 = 108t + -16t2

Solving for variable 't'.

Reorder the terms:
72 + -108t + 16t2 = 108t + -108t + -16t2 + 16t2

Combine like terms: 108t + -108t = 0
72 + -108t + 16t2 = 0 + -16t2 + 16t2
72 + -108t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
72 + -108t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -27t + 4t2) = 0

Factor a trinomial.
4((3 + -4t)(6 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 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 + -4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t = 0 + -3
-4t = 0 + -3

Combine like terms: 0 + -3 = -3
-4t = -3

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
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 = {0.75, 6}