3t^2+t-14=0

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

Simplifying
3t2 + t + -14 = 0

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

Solving
-14 + t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -3t)(2 + -1t) = 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 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

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