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

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

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

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

Combine like terms: 6y + -2y = 4y
4y + -2y2 = 3(y + -2) + 6

Reorder the terms:
4y + -2y2 = 3(-2 + y) + 6
4y + -2y2 = (-2 * 3 + y * 3) + 6
4y + -2y2 = (-6 + 3y) + 6

Reorder the terms:
4y + -2y2 = -6 + 6 + 3y

Combine like terms: -6 + 6 = 0
4y + -2y2 = 0 + 3y
4y + -2y2 = 3y

Solving
4y + -2y2 = 3y

Solving for variable 'y'.

Reorder the terms:
4y + -3y + -2y2 = 3y + -3y

Combine like terms: 4y + -3y = 1y
1y + -2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
1y + -2y2 = 0

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