54=-12(t)+10t^2

Solution for 54=-12(t)+10t^2 equation:

Simplifying
54 = -12(t) + 10t2

Solving
54 = -12t + 10t2

Solving for variable 't'.

Reorder the terms:
54 + 12t + -10t2 = -12t + 12t + 10t2 + -10t2

Combine like terms: -12t + 12t = 0
54 + 12t + -10t2 = 0 + 10t2 + -10t2
54 + 12t + -10t2 = 10t2 + -10t2

Combine like terms: 10t2 + -10t2 = 0
54 + 12t + -10t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 6t + -5t2) = 0

Factor a trinomial.
2((3 + -1t)(9 + 5t)) = 0

Ignore the factor 2.
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 + 5t)' equal to zero and attempt to solve:

Simplifying
9 + 5t = 0

Solving
9 + 5t = 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 + 5t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5t = 0 + -9
5t = 0 + -9

Combine like terms: 0 + -9 = -9
5t = -9

Divide each side by '5'.
t = -1.8

Simplifying
t = -1.8
Solution
t = {3, -1.8}