0=-6t^2+13t+5

Solution for 0=-6t^2+13t+5 equation:

Simplifying
0 = -6t2 + 13t + 5

Reorder the terms:
0 = 5 + 13t + -6t2

Solving
0 = 5 + 13t + -6t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -13t + 6t2 = 5 + 13t + -6t2 + -5 + -13t + 6t2

Reorder the terms:
-5 + -13t + 6t2 = 5 + -5 + 13t + -13t + -6t2 + 6t2

Combine like terms: 5 + -5 = 0
-5 + -13t + 6t2 = 0 + 13t + -13t + -6t2 + 6t2
-5 + -13t + 6t2 = 13t + -13t + -6t2 + 6t2

Combine like terms: 13t + -13t = 0
-5 + -13t + 6t2 = 0 + -6t2 + 6t2
-5 + -13t + 6t2 = -6t2 + 6t2

Combine like terms: -6t2 + 6t2 = 0
-5 + -13t + 6t2 = 0

Factor a trinomial.
(-1 + -3t)(5 + -2t) = 0

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

Simplifying
-1 + -3t = 0

Solving
-1 + -3t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3t = 0 + 1

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

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

Divide each side by '-3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {-0.3333333333, 2.5}