3t^2+13t+14=0

Solution for 3t^2+13t+14=0 equation:

Simplifying
3t2 + 13t + 14 = 0

Reorder the terms:
14 + 13t + 3t2 = 0

Solving
14 + 13t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(7 + 3t)(2 + t) = 0

Subproblem 1
Set the factor '(7 + 3t)' equal to zero and attempt to solve:

Simplifying
7 + 3t = 0

Solving
7 + 3t = 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 + 3t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3t = 0 + -7
3t = 0 + -7

Combine like terms: 0 + -7 = -7
3t = -7

Divide each side by '3'.
t = -2.333333333

Simplifying
t = -2.333333333
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

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

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

Simplifying
t = -2
Solution
t = {-2.333333333, -2}