-3t^2+t+102=0

Solution for -3t^2+t+102=0 equation:

Simplifying
-3t2 + t + 102 = 0

Reorder the terms:
102 + t + -3t2 = 0

Solving
102 + t + -3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + -1t)(17 + 3t) = 0

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

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Subproblem 2
Set the factor '(17 + 3t)' equal to zero and attempt to solve:

Simplifying
17 + 3t = 0

Solving
17 + 3t = 0

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

Add '-17' to each side of the equation.
17 + -17 + 3t = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 3t = 0 + -17
3t = 0 + -17

Combine like terms: 0 + -17 = -17
3t = -17

Divide each side by '3'.
t = -5.666666667

Simplifying
t = -5.666666667
Solution
t = {6, -5.666666667}