2z^2-27z-14=0

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

Simplifying
2z2 + -27z + -14 = 0

Reorder the terms:
-14 + -27z + 2z2 = 0

Solving
-14 + -27z + 2z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-1 + -2z = 0

Solving
-1 + -2z = 0

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

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

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

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

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

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

Simplifying
14 + -1z = 0

Solving
14 + -1z = 0

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

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

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

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

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

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