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

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

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

Reorder the terms:
6y(2 + y) = 3(y + 2)
(2 * 6y + y * 6y) = 3(y + 2)
(12y + 6y2) = 3(y + 2)

Reorder the terms:
12y + 6y2 = 3(2 + y)
12y + 6y2 = (2 * 3 + y * 3)
12y + 6y2 = (6 + 3y)

Solving
12y + 6y2 = 6 + 3y

Solving for variable 'y'.

Reorder the terms:
-6 + 12y + -3y + 6y2 = 6 + 3y + -6 + -3y

Combine like terms: 12y + -3y = 9y
-6 + 9y + 6y2 = 6 + 3y + -6 + -3y

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

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

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

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

Factor a trinomial.
3((-2 + -1y)(1 + -2y)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {-2, 0.5}