z^2=12z-11

Solution for z^2=12z-11 equation:

Simplifying
z2 = 12z + -11

Reorder the terms:
z2 = -11 + 12z

Solving
z2 = -11 + 12z

Solving for variable 'z'.

Reorder the terms:
11 + -12z + z2 = -11 + 12z + 11 + -12z

Reorder the terms:
11 + -12z + z2 = -11 + 11 + 12z + -12z

Combine like terms: -11 + 11 = 0
11 + -12z + z2 = 0 + 12z + -12z
11 + -12z + z2 = 12z + -12z

Combine like terms: 12z + -12z = 0
11 + -12z + z2 = 0

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

Subproblem 1
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
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 = {1, 11}