2y^2-27y-14=0

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

Simplifying
2y2 + -27y + -14 = 0

Reorder the terms:
-14 + -27y + 2y2 = 0

Solving
-14 + -27y + 2y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2y = 0 + 1

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

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

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(14 + -1y)' equal to zero and attempt to solve:

Simplifying
14 + -1y = 0

Solving
14 + -1y = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1y = 0 + -14

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

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

Divide each side by '-1'.
y = 14

Simplifying
y = 14
Solution
y = {-0.5, 14}