0=2t^2-27t-14

Solution for 0=2t^2-27t-14 equation:

Simplifying
0 = 2t2 + -27t + -14

Reorder the terms:
0 = -14 + -27t + 2t2

Solving
0 = -14 + -27t + 2t2

Solving for variable 't'.

Combine like terms: 0 + 14 = 14
14 + 27t + -2t2 = -14 + -27t + 2t2 + 14 + 27t + -2t2

Reorder the terms:
14 + 27t + -2t2 = -14 + 14 + -27t + 27t + 2t2 + -2t2

Combine like terms: -14 + 14 = 0
14 + 27t + -2t2 = 0 + -27t + 27t + 2t2 + -2t2
14 + 27t + -2t2 = -27t + 27t + 2t2 + -2t2

Combine like terms: -27t + 27t = 0
14 + 27t + -2t2 = 0 + 2t2 + -2t2
14 + 27t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
14 + 27t + -2t2 = 0

Factor a trinomial.
(14 + -1t)(1 + 2t) = 0

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

Simplifying
14 + -1t = 0

Solving
14 + -1t = 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 + -1t = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1t = 0 + -14
-1t = 0 + -14

Combine like terms: 0 + -14 = -14
-1t = -14

Divide each side by '-1'.
t = 14

Simplifying
t = 14
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 = {14, -0.5}