4z^2-16z+16=0

Solution for 4z^2-16z+16=0 equation:

Simplifying
4z2 + -16z + 16 = 0

Reorder the terms:
16 + -16z + 4z2 = 0

Solving
16 + -16z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -4z + z2) = 0

Factor a trinomial.
4((2 + -1z)(2 + -1z)) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {2, 2}