3z^2-2z+z^2=

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

Simplifying
3z2 + -2z + z2 = 0

Reorder the terms:
-2z + 3z2 + z2 = 0

Combine like terms: 3z2 + z2 = 4z2
-2z + 4z2 = 0

Solving
-2z + 4z2 = 0

Solving for variable 'z'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-1 + 2z)' equal to zero and attempt to solve:

Simplifying
-1 + 2z = 0

Solving
-1 + 2z = 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 + 2z = 0 + 1

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

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

Divide each side by '2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {0, 0.5}