3y^2=6y-3

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

Simplifying
3y2 = 6y + -3

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

Solving
3y2 = -3 + 6y

Solving for variable 'y'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2y + y2) = 0

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

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

Simplifying
1 + -1y = 0

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

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

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

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

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {1, 1}