2((9+y)(2+y))=0

Solution for 2((9+y)(2+y))=0 equation:

Simplifying
2((9 + y)(2 + y)) = 0

Multiply (9 + y) * (2 + y)
2((9(2 + y) + y(2 + y))) = 0
2(((2 * 9 + y * 9) + y(2 + y))) = 0
2(((18 + 9y) + y(2 + y))) = 0
2((18 + 9y + (2 * y + y * y))) = 0
2((18 + 9y + (2y + y2))) = 0

Combine like terms: 9y + 2y = 11y
2((18 + 11y + y2)) = 0
(18 * 2 + 11y * 2 + y2 * 2) = 0
(36 + 22y + 2y2) = 0

Solving
36 + 22y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 11y + y2) = 0

Factor a trinomial.
2((9 + y)(2 + y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

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

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

Simplifying
y = -9
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {-9, -2}