4z^2+88z-92=0

Solution for 4z^2+88z-92=0 equation:

Simplifying
4z2 + 88z + -92 = 0

Reorder the terms:
-92 + 88z + 4z2 = 0

Solving
-92 + 88z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + 22z + z2) = 0

Factor a trinomial.
4((-23 + -1z)(1 + -1z)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-23 + -1z)' equal to zero and attempt to solve:

Simplifying
-23 + -1z = 0

Solving
-23 + -1z = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1z = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1z = 0 + 23
-1z = 0 + 23

Combine like terms: 0 + 23 = 23
-1z = 23

Divide each side by '-1'.
z = -23

Simplifying
z = -23
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 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 + -1z = 0 + -1

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

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

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

Simplifying
z = 1
Solution
z = {-23, 1}