5t^2+11t+6=0

Solution for 5t^2+11t+6=0 equation:

Simplifying
5t2 + 11t + 6 = 0

Reorder the terms:
6 + 11t + 5t2 = 0

Solving
6 + 11t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + 5t)(1 + t) = 0

Subproblem 1
Set the factor '(6 + 5t)' equal to zero and attempt to solve:

Simplifying
6 + 5t = 0

Solving
6 + 5t = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5t = 0 + -6

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

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

Divide each side by '5'.
t = -1.2

Simplifying
t = -1.2
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 = {-1.2, -1}