3y-6y^2z=0

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

Simplifying
3y + -6y2z = 0

Solving
3y + -6y2z = 0

Solving for variable 'y'.

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

Ignore the factor 3.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

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

Simplifying
1 + -2yz = 0

Solving
1 + -2yz = 0

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

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

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

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

Divide each side by '-2z'.
y = 0.5z-1

Simplifying
y = 0.5z-1
Solution
y = {0, 0.5z-1}