y^2+4y+16=-5y-2

Solution for y^2+4y+16=-5y-2 equation:

Simplifying
y2 + 4y + 16 = -5y + -2

Reorder the terms:
16 + 4y + y2 = -5y + -2

Reorder the terms:
16 + 4y + y2 = -2 + -5y

Solving
16 + 4y + y2 = -2 + -5y

Solving for variable 'y'.

Reorder the terms:
16 + 2 + 4y + 5y + y2 = -2 + -5y + 2 + 5y

Combine like terms: 16 + 2 = 18
18 + 4y + 5y + y2 = -2 + -5y + 2 + 5y

Combine like terms: 4y + 5y = 9y
18 + 9y + y2 = -2 + -5y + 2 + 5y

Reorder the terms:
18 + 9y + y2 = -2 + 2 + -5y + 5y

Combine like terms: -2 + 2 = 0
18 + 9y + y2 = 0 + -5y + 5y
18 + 9y + y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
18 + 9y + y2 = 0

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

Subproblem 1
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
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 = {-6, -3}