z^2-8z+16=64

Solution for z^2-8z+16=64 equation:

Simplifying
z2 + -8z + 16 = 64

Reorder the terms:
16 + -8z + z2 = 64

Solving
16 + -8z + z2 = 64

Solving for variable 'z'.

Reorder the terms:
16 + -64 + -8z + z2 = 64 + -64

Combine like terms: 16 + -64 = -48
-48 + -8z + z2 = 64 + -64

Combine like terms: 64 + -64 = 0
-48 + -8z + z2 = 0

Factor a trinomial.
(-4 + -1z)(12 + -1z) = 0

Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(12 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

Simplifying
z = 12
Solution
z = {-4, 12}