9t^2-72t+108=0

Solution for 9t^2-72t+108=0 equation:

Simplifying
9t2 + -72t + 108 = 0

Reorder the terms:
108 + -72t + 9t2 = 0

Solving
108 + -72t + 9t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '9'.
9(12 + -8t + t2) = 0

Factor a trinomial.
9((2 + -1t)(6 + -1t)) = 0

Ignore the factor 9.
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}