-t^2+11t+102=0

Solution for -t^2+11t+102=0 equation:

Simplifying
-1t2 + 11t + 102 = 0

Reorder the terms:
102 + 11t + -1t2 = 0

Solving
102 + 11t + -1t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(17 + -1t)' equal to zero and attempt to solve:

Simplifying
17 + -1t = 0

Solving
17 + -1t = 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 + -1t = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1t = 0 + -17
-1t = 0 + -17

Combine like terms: 0 + -17 = -17
-1t = -17

Divide each side by '-1'.
t = 17

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

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

Simplifying
t = -6
Solution
t = {17, -6}