2z^2-16z-1768=0

Solution for 2z^2-16z-1768=0 equation:

Simplifying
2z2 + -16z + -1768 = 0

Reorder the terms:
-1768 + -16z + 2z2 = 0

Solving
-1768 + -16z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-884 + -8z + z2) = 0

Factor a trinomial.
2((-26 + -1z)(34 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-26 + -1z)' equal to zero and attempt to solve:

Simplifying
-26 + -1z = 0

Solving
-26 + -1z = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1z = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1z = 0 + 26
-1z = 0 + 26

Combine like terms: 0 + 26 = 26
-1z = 26

Divide each side by '-1'.
z = -26

Simplifying
z = -26
Subproblem 2
Set the factor '(34 + -1z)' equal to zero and attempt to solve:

Simplifying
34 + -1z = 0

Solving
34 + -1z = 0

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

Add '-34' to each side of the equation.
34 + -34 + -1z = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -1z = 0 + -34
-1z = 0 + -34

Combine like terms: 0 + -34 = -34
-1z = -34

Divide each side by '-1'.
z = 34

Simplifying
z = 34
Solution
z = {-26, 34}