y(y+5)=-6

Solution for y(y+5)=-6 equation:

Simplifying
y(y + 5) = -6

Reorder the terms:
y(5 + y) = -6
(5 * y + y * y) = -6
(5y + y2) = -6

Solving
5y + y2 = -6

Solving for variable 'y'.

Reorder the terms:
6 + 5y + y2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 5y + y2 = 0

Factor a trinomial.
(3 + y)(2 + 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 '(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 = {-3, -2}