3z^2-6z+6=0

Solution for 3z^2-6z+6=0 equation:

Simplifying
3z2 + -6z + 6 = 0

Reorder the terms:
6 + -6z + 3z2 = 0

Solving
6 + -6z + 3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -2z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -2z + z2)' equal to zero and attempt to solve:

Simplifying
2 + -2z + z2 = 0

Solving
2 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + -2z + z2 = 0 + -2

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

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

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = -2 + 1

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

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

Factor a perfect square on the left side:
(z + -1)(z + -1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.