3y(y-2)=6(y-1)-3y

Solution for 3y(y-2)=6(y-1)-3y equation:

Simplifying
3y(y + -2) = 6(y + -1) + -3y

Reorder the terms:
3y(-2 + y) = 6(y + -1) + -3y
(-2 * 3y + y * 3y) = 6(y + -1) + -3y
(-6y + 3y2) = 6(y + -1) + -3y

Reorder the terms:
-6y + 3y2 = 6(-1 + y) + -3y
-6y + 3y2 = (-1 * 6 + y * 6) + -3y
-6y + 3y2 = (-6 + 6y) + -3y

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

Solving
-6y + 3y2 = -6 + 3y

Solving for variable 'y'.

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

Combine like terms: -6y + -3y = -9y
6 + -9y + 3y2 = -6 + 3y + 6 + -3y

Reorder the terms:
6 + -9y + 3y2 = -6 + 6 + 3y + -3y

Combine like terms: -6 + 6 = 0
6 + -9y + 3y2 = 0 + 3y + -3y
6 + -9y + 3y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
6 + -9y + 3y2 = 0

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

Factor a trinomial.
3((1 + -1y)(2 + -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 '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

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

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

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

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

Simplifying
y = 2
Solution
y = {1, 2}