(a+3)(2a+4)=

Solution for (a+3)(2a+4)= equation:

Simplifying
(a + 3)(2a + 4) = 0

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

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

Multiply (3 + a) * (4 + 2a)
(3(4 + 2a) + a(4 + 2a)) = 0
((4 * 3 + 2a * 3) + a(4 + 2a)) = 0
((12 + 6a) + a(4 + 2a)) = 0
(12 + 6a + (4 * a + 2a * a)) = 0
(12 + 6a + (4a + 2a2)) = 0

Combine like terms: 6a + 4a = 10a
(12 + 10a + 2a2) = 0

Solving
12 + 10a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5a + a2) = 0

Factor a trinomial.
2((3 + a)(2 + a)) = 0

Ignore the factor 2.
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 '(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 = {-3, -2}