-2t^2-5t+33=0

Solution for -2t^2-5t+33=0 equation:

Simplifying
-2t2 + -5t + 33 = 0

Reorder the terms:
33 + -5t + -2t2 = 0

Solving
33 + -5t + -2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -1t)(11 + 2t) = 0

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 '(11 + 2t)' equal to zero and attempt to solve:

Simplifying
11 + 2t = 0

Solving
11 + 2t = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2t = 0 + -11
2t = 0 + -11

Combine like terms: 0 + -11 = -11
2t = -11

Divide each side by '2'.
t = -5.5

Simplifying
t = -5.5
Solution
t = {3, -5.5}