14z^2-51z-54=0

Solution for 14z^2-51z-54=0 equation:

Simplifying
14z2 + -51z + -54 = 0

Reorder the terms:
-54 + -51z + 14z2 = 0

Solving
-54 + -51z + 14z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -7z)(9 + -2z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -2z)' equal to zero and attempt to solve:

Simplifying
9 + -2z = 0

Solving
9 + -2z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2z = 0 + -9
-2z = 0 + -9

Combine like terms: 0 + -9 = -9
-2z = -9

Divide each side by '-2'.
z = 4.5

Simplifying
z = 4.5
Solution
z = {-0.8571428571, 4.5}