(a+6)(a+4)=0

Solution for (a+6)(a+4)=0 equation:

Simplifying
(a + 6)(a + 4) = 0

Reorder the terms:
(6 + a)(a + 4) = 0

Reorder the terms:
(6 + a)(4 + a) = 0

Multiply (6 + a) * (4 + a)
(6(4 + a) + a(4 + a)) = 0
((4 * 6 + a * 6) + a(4 + a)) = 0
((24 + 6a) + a(4 + a)) = 0
(24 + 6a + (4 * a + a * a)) = 0
(24 + 6a + (4a + a2)) = 0

Combine like terms: 6a + 4a = 10a
(24 + 10a + a2) = 0

Solving
24 + 10a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(4 + a) = 0

Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Solution
a = {-6, -4}