-2t^2+24t-54=0

Solution for -2t^2+24t-54=0 equation:

Simplifying
-2t2 + 24t + -54 = 0

Reorder the terms:
-54 + 24t + -2t2 = 0

Solving
-54 + 24t + -2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 12t + -1t2) = 0

Factor a trinomial.
2((-9 + t)(3 + -1t)) = 0

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

Simplifying
-9 + t = 0

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

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

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

Simplifying
t = 9
Subproblem 2
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
Solution
t = {9, 3}