(2+2a)(3+6a)=

Solution for (2+2a)(3+6a)= equation:

Simplifying
(2 + 2a)(3 + 6a) = 0

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

Combine like terms: 12a + 6a = 18a
(6 + 18a + 12a2) = 0

Solving
6 + 18a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 3a + 2a2) = 0

Factor a trinomial.
6((1 + a)(1 + 2a)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-1, -0.5}