z^2-6z-307=8

Solution for z^2-6z-307=8 equation:

Simplifying
z2 + -6z + -307 = 8

Reorder the terms:
-307 + -6z + z2 = 8

Solving
-307 + -6z + z2 = 8

Solving for variable 'z'.

Reorder the terms:
-307 + -8 + -6z + z2 = 8 + -8

Combine like terms: -307 + -8 = -315
-315 + -6z + z2 = 8 + -8

Combine like terms: 8 + -8 = 0
-315 + -6z + z2 = 0

Factor a trinomial.
(-15 + -1z)(21 + -1z) = 0

Subproblem 1
Set the factor '(-15 + -1z)' equal to zero and attempt to solve:

Simplifying
-15 + -1z = 0

Solving
-15 + -1z = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1z = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1z = 0 + 15
-1z = 0 + 15

Combine like terms: 0 + 15 = 15
-1z = 15

Divide each side by '-1'.
z = -15

Simplifying
z = -15
Subproblem 2
Set the factor '(21 + -1z)' equal to zero and attempt to solve:

Simplifying
21 + -1z = 0

Solving
21 + -1z = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1z = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1z = 0 + -21
-1z = 0 + -21

Combine like terms: 0 + -21 = -21
-1z = -21

Divide each side by '-1'.
z = 21

Simplifying
z = 21
Solution
z = {-15, 21}