(y+3)(y+3)=9

Solution for (y+3)(y+3)=9 equation:

Simplifying
(y + 3)(y + 3) = 9

Reorder the terms:
(3 + y)(y + 3) = 9

Reorder the terms:
(3 + y)(3 + y) = 9

Multiply (3 + y) * (3 + y)
(3(3 + y) + y(3 + y)) = 9
((3 * 3 + y * 3) + y(3 + y)) = 9
((9 + 3y) + y(3 + y)) = 9
(9 + 3y + (3 * y + y * y)) = 9
(9 + 3y + (3y + y2)) = 9

Combine like terms: 3y + 3y = 6y
(9 + 6y + y2) = 9

Add '-9' to each side of the equation.
9 + 6y + -9 + y2 = 9 + -9

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

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

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

Solving
6y + y2 = 0

Solving for variable 'y'.

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

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 '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

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

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

Simplifying
y = -6
Solution
y = {0, -6}