(2a+4)(a+6)=

Solution for (2a+4)(a+6)= equation:

Simplifying
(2a + 4)(a + 6) = 0

Reorder the terms:
(4 + 2a)(a + 6) = 0

Reorder the terms:
(4 + 2a)(6 + a) = 0

Multiply (4 + 2a) * (6 + a)
(4(6 + a) + 2a * (6 + a)) = 0
((6 * 4 + a * 4) + 2a * (6 + a)) = 0
((24 + 4a) + 2a * (6 + a)) = 0
(24 + 4a + (6 * 2a + a * 2a)) = 0
(24 + 4a + (12a + 2a2)) = 0

Combine like terms: 4a + 12a = 16a
(24 + 16a + 2a2) = 0

Solving
24 + 16a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 8a + a2) = 0

Factor a trinomial.
2((6 + a)(2 + a)) = 0

Ignore the factor 2.
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 '(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 = {-6, -2}