14T^2-3T-2=0

Solution for 14T^2-3T-2=0 equation:

Simplifying
14T2 + -3T + -2 = 0

Reorder the terms:
-2 + -3T + 14T2 = 0

Solving
-2 + -3T + 14T2 = 0

Solving for variable 'T'.

Factor a trinomial.
(-2 + -7T)(1 + -2T) = 0

Subproblem 1
Set the factor '(-2 + -7T)' equal to zero and attempt to solve:

Simplifying
-2 + -7T = 0

Solving
-2 + -7T = 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 + -7T = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7T = 0 + 2
-7T = 0 + 2

Combine like terms: 0 + 2 = 2
-7T = 2

Divide each side by '-7'.
T = -0.2857142857

Simplifying
T = -0.2857142857
Subproblem 2
Set the factor '(1 + -2T)' equal to zero and attempt to solve:

Simplifying
1 + -2T = 0

Solving
1 + -2T = 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 + -2T = 0 + -1

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

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

Divide each side by '-2'.
T = 0.5

Simplifying
T = 0.5
Solution
T = {-0.2857142857, 0.5}