(y+5)(y+2)=0

Solution for (y+5)(y+2)=0 equation:

Simplifying
(y + 5)(y + 2) = 0

Reorder the terms:
(5 + y)(y + 2) = 0

Reorder the terms:
(5 + y)(2 + y) = 0

Multiply (5 + y) * (2 + y)
(5(2 + y) + y(2 + y)) = 0
((2 * 5 + y * 5) + y(2 + y)) = 0
((10 + 5y) + y(2 + y)) = 0
(10 + 5y + (2 * y + y * y)) = 0
(10 + 5y + (2y + y2)) = 0

Combine like terms: 5y + 2y = 7y
(10 + 7y + y2) = 0

Solving
10 + 7y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + y)(2 + y) = 0

Subproblem 1
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
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 = {-5, -2}