3t^2+43t+14=0

Solution for 3t^2+43t+14=0 equation:

Simplifying
3t2 + 43t + 14 = 0

Reorder the terms:
14 + 43t + 3t2 = 0

Solving
14 + 43t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(14 + t)(1 + 3t) = 0

Subproblem 1
Set the factor '(14 + t)' equal to zero and attempt to solve:

Simplifying
14 + t = 0

Solving
14 + t = 0

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

Add '-14' to each side of the equation.
14 + -14 + t = 0 + -14

Combine like terms: 14 + -14 = 0
0 + t = 0 + -14
t = 0 + -14

Combine like terms: 0 + -14 = -14
t = -14

Simplifying
t = -14
Subproblem 2
Set the factor '(1 + 3t)' equal to zero and attempt to solve:

Simplifying
1 + 3t = 0

Solving
1 + 3t = 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 + 3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3t = 0 + -1
3t = 0 + -1

Combine like terms: 0 + -1 = -1
3t = -1

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Solution
t = {-14, -0.3333333333}