z^2-2z=323

Solution for z^2-2z=323 equation:

Simplifying
z2 + -2z = 323

Reorder the terms:
-2z + z2 = 323

Solving
-2z + z2 = 323

Solving for variable 'z'.

Reorder the terms:
-323 + -2z + z2 = 323 + -323

Combine like terms: 323 + -323 = 0
-323 + -2z + z2 = 0

Factor a trinomial.
(-17 + -1z)(19 + -1z) = 0

Subproblem 1
Set the factor '(-17 + -1z)' equal to zero and attempt to solve:

Simplifying
-17 + -1z = 0

Solving
-17 + -1z = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1z = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1z = 0 + 17
-1z = 0 + 17

Combine like terms: 0 + 17 = 17
-1z = 17

Divide each side by '-1'.
z = -17

Simplifying
z = -17
Subproblem 2
Set the factor '(19 + -1z)' equal to zero and attempt to solve:

Simplifying
19 + -1z = 0

Solving
19 + -1z = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1z = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1z = 0 + -19
-1z = 0 + -19

Combine like terms: 0 + -19 = -19
-1z = -19

Divide each side by '-1'.
z = 19

Simplifying
z = 19
Solution
z = {-17, 19}