y^2+12y=-27

Solution for y^2+12y=-27 equation:

Simplifying
y2 + 12y = -27

Reorder the terms:
12y + y2 = -27

Solving
12y + y2 = -27

Solving for variable 'y'.

Reorder the terms:
27 + 12y + y2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 12y + y2 = 0

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

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 '(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 = {-9, -3}