z^2-2z+1=64

Solution for z^2-2z+1=64 equation:

Simplifying
z2 + -2z + 1 = 64

Reorder the terms:
1 + -2z + z2 = 64

Solving
1 + -2z + z2 = 64

Solving for variable 'z'.

Reorder the terms:
1 + -64 + -2z + z2 = 64 + -64

Combine like terms: 1 + -64 = -63
-63 + -2z + z2 = 64 + -64

Combine like terms: 64 + -64 = 0
-63 + -2z + z2 = 0

Factor a trinomial.
(-7 + -1z)(9 + -1z) = 0

Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Solution
z = {-7, 9}