-18t^2+72t-54=0

Solution for -18t^2+72t-54=0 equation:

Simplifying
-18t2 + 72t + -54 = 0

Reorder the terms:
-54 + 72t + -18t2 = 0

Solving
-54 + 72t + -18t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-3 + 4t + -1t2) = 0

Factor a trinomial.
18((-3 + t)(1 + -1t)) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(-3 + t)' equal to zero and attempt to solve:

Simplifying
-3 + t = 0

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

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

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

Simplifying
t = 3
Subproblem 2
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
Solution
t = {3, 1}