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

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

Simplifying
6(y + -1) + 3(-2y + 2) * y = 0

Reorder the terms:
6(-1 + y) + 3(-2y + 2) * y = 0
(-1 * 6 + y * 6) + 3(-2y + 2) * y = 0
(-6 + 6y) + 3(-2y + 2) * y = 0

Reorder the terms:
-6 + 6y + 3(2 + -2y) * y = 0

Reorder the terms for easier multiplication:
-6 + 6y + 3y(2 + -2y) = 0
-6 + 6y + (2 * 3y + -2y * 3y) = 0
-6 + 6y + (6y + -6y2) = 0

Combine like terms: 6y + 6y = 12y
-6 + 12y + -6y2 = 0

Solving
-6 + 12y + -6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2y + -1y2) = 0

Factor a trinomial.
6((-1 + y)(1 + -1y)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + y)' equal to zero and attempt to solve:

Simplifying
-1 + y = 0

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

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

Combine like terms: 0 + 1 = 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}