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

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

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

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

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

Multiply (6 + 2a) * (4 + 4a)
(6(4 + 4a) + 2a * (4 + 4a)) = 0
((4 * 6 + 4a * 6) + 2a * (4 + 4a)) = 0
((24 + 24a) + 2a * (4 + 4a)) = 0
(24 + 24a + (4 * 2a + 4a * 2a)) = 0
(24 + 24a + (8a + 8a2)) = 0

Combine like terms: 24a + 8a = 32a
(24 + 32a + 8a2) = 0

Solving
24 + 32a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(3 + 4a + a2) = 0

Factor a trinomial.
8((3 + a)(1 + a)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

Add '-1' to each side of the equation.
1 + -1 + a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Solution
a = {-3, -1}