y(y+5)+6(y+5)=0

Solution for y(y+5)+6(y+5)=0 equation:

Simplifying
y(y + 5) + 6(y + 5) = 0

Reorder the terms:
y(5 + y) + 6(y + 5) = 0
(5 * y + y * y) + 6(y + 5) = 0
(5y + y2) + 6(y + 5) = 0

Reorder the terms:
5y + y2 + 6(5 + y) = 0
5y + y2 + (5 * 6 + y * 6) = 0
5y + y2 + (30 + 6y) = 0

Reorder the terms:
30 + 5y + 6y + y2 = 0

Combine like terms: 5y + 6y = 11y
30 + 11y + y2 = 0

Solving
30 + 11y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(5 + 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 '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

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

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

Simplifying
y = -5
Solution
y = {-6, -5}