0=3y-6y^2

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

Simplifying
0 = 3y + -6y2

Solving
0 = 3y + -6y2

Solving for variable 'y'.
Remove the zero:
-3y + 6y2 = 3y + -6y2 + -3y + 6y2

Reorder the terms:
-3y + 6y2 = 3y + -3y + -6y2 + 6y2

Combine like terms: 3y + -3y = 0
-3y + 6y2 = 0 + -6y2 + 6y2
-3y + 6y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
-3y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-1 + 2y) = 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 + 2y)' equal to zero and attempt to solve:

Simplifying
-1 + 2y = 0

Solving
-1 + 2y = 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 + 2y = 0 + 1

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

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

Divide each side by '2'.
y = 0.5

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