(3y+6)(3y+6)=36

Solution for (3y+6)(3y+6)=36 equation:

Simplifying
(3y + 6)(3y + 6) = 36

Reorder the terms:
(6 + 3y)(3y + 6) = 36

Reorder the terms:
(6 + 3y)(6 + 3y) = 36

Multiply (6 + 3y) * (6 + 3y)
(6(6 + 3y) + 3y * (6 + 3y)) = 36
((6 * 6 + 3y * 6) + 3y * (6 + 3y)) = 36
((36 + 18y) + 3y * (6 + 3y)) = 36
(36 + 18y + (6 * 3y + 3y * 3y)) = 36
(36 + 18y + (18y + 9y2)) = 36

Combine like terms: 18y + 18y = 36y
(36 + 36y + 9y2) = 36

Add '-36' to each side of the equation.
36 + 36y + -36 + 9y2 = 36 + -36

Reorder the terms:
36 + -36 + 36y + 9y2 = 36 + -36

Combine like terms: 36 + -36 = 0
0 + 36y + 9y2 = 36 + -36
36y + 9y2 = 36 + -36

Combine like terms: 36 + -36 = 0
36y + 9y2 = 0

Solving
36y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9y'.
9y(4 + y) = 0

Ignore the factor 9.
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 '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {0, -4}