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

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

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

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

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

Solving
12y + 12y2 = 6 + 6y

Solving for variable 'y'.

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

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

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

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

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

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

Factor a trinomial.
6((-1 + -1y)(1 + -2y)) = 0

Ignore the factor 6.
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 '(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 = {-1, 0.5}