2t^2+27t-14=0

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

Simplifying
2t2 + 27t + -14 = 0

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

Solving
-14 + 27t + 2t2 = 0

Solving for variable 't'.

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}