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

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

Simplifying
2(a2 + a)(3a2 + 6a) = 0

Reorder the terms:
2(a + a2)(3a2 + 6a) = 0

Reorder the terms:
2(a + a2)(6a + 3a2) = 0

Multiply (a + a2) * (6a + 3a2)
2(a(6a + 3a2) + a2(6a + 3a2)) = 0
2((6a * a + 3a2 * a) + a2(6a + 3a2)) = 0
2((6a2 + 3a3) + a2(6a + 3a2)) = 0
2(6a2 + 3a3 + (6a * a2 + 3a2 * a2)) = 0
2(6a2 + 3a3 + (6a3 + 3a4)) = 0

Combine like terms: 3a3 + 6a3 = 9a3
2(6a2 + 9a3 + 3a4) = 0
(6a2 * 2 + 9a3 * 2 + 3a4 * 2) = 0
(12a2 + 18a3 + 6a4) = 0

Solving
12a2 + 18a3 + 6a4 = 0

Solving for variable 'a'.

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

Factor a trinomial.
6a2((2 + a)(1 + a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
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
Subproblem 3
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 = {0, -2, -1}