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.
(3 + -1t)(2 + 5t) = 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 '(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
Solution
t = {3, -0.4}