6t^2+13t+7=0

Solution for 6t^2+13t+7=0 equation:

Simplifying
6t2 + 13t + 7 = 0

Reorder the terms:
7 + 13t + 6t2 = 0

Solving
7 + 13t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(7 + 6t)(1 + t) = 0

Subproblem 1
Set the factor '(7 + 6t)' equal to zero and attempt to solve:

Simplifying
7 + 6t = 0

Solving
7 + 6t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 6t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6t = 0 + -7
6t = 0 + -7

Combine like terms: 0 + -7 = -7
6t = -7

Divide each side by '6'.
t = -1.166666667

Simplifying
t = -1.166666667
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 = {-1.166666667, -1}