z^2-4z-77=0

Solution for z^2-4z-77=0 equation:

Simplifying
z2 + -4z + -77 = 0

Reorder the terms:
-77 + -4z + z2 = 0

Solving
-77 + -4z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(11 + -1z) = 0

Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(11 + -1z)' equal to zero and attempt to solve:

Simplifying
11 + -1z = 0

Solving
11 + -1z = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z = 0 + -11
-1z = 0 + -11

Combine like terms: 0 + -11 = -11
-1z = -11

Divide each side by '-1'.
z = 11

Simplifying
z = 11
Solution
z = {-7, 11}