14z^2-5z-6=0

Solution for 14z^2-5z-6=0 equation:

Simplifying
14z2 + -5z + -6 = 0

Reorder the terms:
-6 + -5z + 14z2 = 0

Solving
-6 + -5z + 14z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -2z)(6 + -7z) = 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 '(6 + -7z)' equal to zero and attempt to solve:

Simplifying
6 + -7z = 0

Solving
6 + -7z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7z = 0 + -6
-7z = 0 + -6

Combine like terms: 0 + -6 = -6
-7z = -6

Divide each side by '-7'.
z = 0.8571428571

Simplifying
z = 0.8571428571
Solution
z = {-0.5, 0.8571428571}