0=102+t-3t^2

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

Simplifying
0 = 102 + t + -3t2

Solving
0 = 102 + t + -3t2

Solving for variable 't'.

Combine like terms: 0 + -102 = -102
-102 + -1t + 3t2 = 102 + t + -3t2 + -102 + -1t + 3t2

Reorder the terms:
-102 + -1t + 3t2 = 102 + -102 + t + -1t + -3t2 + 3t2

Combine like terms: 102 + -102 = 0
-102 + -1t + 3t2 = 0 + t + -1t + -3t2 + 3t2
-102 + -1t + 3t2 = t + -1t + -3t2 + 3t2

Combine like terms: t + -1t = 0
-102 + -1t + 3t2 = 0 + -3t2 + 3t2
-102 + -1t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
-102 + -1t + 3t2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
t = {-5.666666667, 6}