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

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

Simplifying
0 = -5t2 + 13t + 6

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

Solving
0 = 6 + 13t + -5t2

Solving for variable 't'.

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

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

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

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

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

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

Subproblem 1
Set the factor '(-2 + -5t)' equal to zero and attempt to solve:

Simplifying
-2 + -5t = 0

Solving
-2 + -5t = 0

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

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

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

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

Divide each side by '-5'.
t = -0.4

Simplifying
t = -0.4
Subproblem 2
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
Solution
t = {-0.4, 3}