6t^2-31t+33=0

Solution for 6t^2-31t+33=0 equation:

Simplifying
6t2 + -31t + 33 = 0

Reorder the terms:
33 + -31t + 6t2 = 0

Solving
33 + -31t + 6t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(11 + -3t)' equal to zero and attempt to solve:

Simplifying
11 + -3t = 0

Solving
11 + -3t = 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 + -3t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3t = 0 + -11
-3t = 0 + -11

Combine like terms: 0 + -11 = -11
-3t = -11

Divide each side by '-3'.
t = 3.666666667

Simplifying
t = 3.666666667
Solution
t = {1.5, 3.666666667}