-3z^2+6z-3=0

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

Simplifying
-3z2 + 6z + -3 = 0

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

Solving
-3 + 6z + -3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2z + -1z2) = 0

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

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

Simplifying
-1 + z = 0

Solving
-1 + z = 0

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

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

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

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Solution
z = {1, 1}