z^2+85z-546=0

Solution for z^2+85z-546=0 equation:

Simplifying
z2 + 85z + -546 = 0

Reorder the terms:
-546 + 85z + z2 = 0

Solving
-546 + 85z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-91 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-91 + -1z)' equal to zero and attempt to solve:

Simplifying
-91 + -1z = 0

Solving
-91 + -1z = 0

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

Add '91' to each side of the equation.
-91 + 91 + -1z = 0 + 91

Combine like terms: -91 + 91 = 0
0 + -1z = 0 + 91
-1z = 0 + 91

Combine like terms: 0 + 91 = 91
-1z = 91

Divide each side by '-1'.
z = -91

Simplifying
z = -91
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-91, 6}