y(y+6)=-9

Solution for y(y+6)=-9 equation:

Simplifying
y(y + 6) = -9

Reorder the terms:
y(6 + y) = -9
(6 * y + y * y) = -9
(6y + y2) = -9

Solving
6y + y2 = -9

Solving for variable 'y'.

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

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

Factor a trinomial.
(3 + y)(3 + y) = 0

Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {-3, -3}