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

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

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

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

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

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

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

Solving
6y + 6y2 = 3y

Solving for variable 'y'.

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

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

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

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

Ignore the factor 3.
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}