(a+2)(a+5)=0

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

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

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

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

Multiply (2 + a) * (5 + a)
(2(5 + a) + a(5 + a)) = 0
((5 * 2 + a * 2) + a(5 + a)) = 0
((10 + 2a) + a(5 + a)) = 0
(10 + 2a + (5 * a + a * a)) = 0
(10 + 2a + (5a + a2)) = 0

Combine like terms: 2a + 5a = 7a
(10 + 7a + a2) = 0

Solving
10 + 7a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

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

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

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

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

Simplifying
a = -5
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {-5, -2}