12t^2-66t+54=0

Solution for 12t^2-66t+54=0 equation:

Simplifying
12t2 + -66t + 54 = 0

Reorder the terms:
54 + -66t + 12t2 = 0

Solving
54 + -66t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + -11t + 2t2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

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

Simplifying
9 + -2t = 0

Solving
9 + -2t = 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 + -2t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2t = 0 + -9
-2t = 0 + -9

Combine like terms: 0 + -9 = -9
-2t = -9

Divide each side by '-2'.
t = 4.5

Simplifying
t = 4.5
Solution
t = {1, 4.5}