3y^2-2y+6=6

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

Simplifying
3y2 + -2y + 6 = 6

Reorder the terms:
6 + -2y + 3y2 = 6

Add '-6' to each side of the equation.
6 + -2y + -6 + 3y2 = 6 + -6

Reorder the terms:
6 + -6 + -2y + 3y2 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + -2y + 3y2 = 6 + -6
-2y + 3y2 = 6 + -6

Combine like terms: 6 + -6 = 0
-2y + 3y2 = 0

Solving
-2y + 3y2 = 0

Solving for variable 'y'.

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

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 '(-2 + 3y)' equal to zero and attempt to solve:

Simplifying
-2 + 3y = 0

Solving
-2 + 3y = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3y = 0 + 2
3y = 0 + 2

Combine like terms: 0 + 2 = 2
3y = 2

Divide each side by '3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {0, 0.6666666667}