4t^2-48t+108=0

Solution for 4t^2-48t+108=0 equation:

Simplifying
4t2 + -48t + 108 = 0

Reorder the terms:
108 + -48t + 4t2 = 0

Solving
108 + -48t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + -12t + t2) = 0

Factor a trinomial.
4((3 + -1t)(9 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {3, 9}