z^2=6z-9

Solution for z^2=6z-9 equation:

Simplifying
z2 = 6z + -9

Reorder the terms:
z2 = -9 + 6z

Solving
z2 = -9 + 6z

Solving for variable 'z'.

Reorder the terms:
9 + -6z + z2 = -9 + 6z + 9 + -6z

Reorder the terms:
9 + -6z + z2 = -9 + 9 + 6z + -6z

Combine like terms: -9 + 9 = 0
9 + -6z + z2 = 0 + 6z + -6z
9 + -6z + z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
9 + -6z + z2 = 0

Factor a trinomial.
(3 + -1z)(3 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {3, 3}