5t^2+13t+8=0

Solution for 5t^2+13t+8=0 equation:

Simplifying
5t2 + 13t + 8 = 0

Reorder the terms:
8 + 13t + 5t2 = 0

Solving
8 + 13t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(8 + 5t)(1 + t) = 0

Subproblem 1
Set the factor '(8 + 5t)' equal to zero and attempt to solve:

Simplifying
8 + 5t = 0

Solving
8 + 5t = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5t = 0 + -8
5t = 0 + -8

Combine like terms: 0 + -8 = -8
5t = -8

Divide each side by '5'.
t = -1.6

Simplifying
t = -1.6
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 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 + t = 0 + -1

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

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

Simplifying
t = -1
Solution
t = {-1.6, -1}