5a*(3a+2)*(a+2)=0

Solution for 5a*(3a+2)*(a+2)=0 equation:

Simplifying
5a(3a + 2)(a + 2) = 0

Reorder the terms:
5a(2 + 3a)(a + 2) = 0

Reorder the terms:
5a(2 + 3a)(2 + a) = 0

Multiply (2 + 3a) * (2 + a)
5a(2(2 + a) + 3a * (2 + a)) = 0
5a((2 * 2 + a * 2) + 3a * (2 + a)) = 0
5a((4 + 2a) + 3a * (2 + a)) = 0
5a(4 + 2a + (2 * 3a + a * 3a)) = 0
5a(4 + 2a + (6a + 3a2)) = 0

Combine like terms: 2a + 6a = 8a
5a(4 + 8a + 3a2) = 0
(4 * 5a + 8a * 5a + 3a2 * 5a) = 0
(20a + 40a2 + 15a3) = 0

Solving
20a + 40a2 + 15a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a'.
5a(4 + 8a + 3a2) = 0

Factor a trinomial.
5a((2 + a)(2 + 3a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
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 '(2 + 3a)' equal to zero and attempt to solve:

Simplifying
2 + 3a = 0

Solving
2 + 3a = 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 + 3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a = 0 + -2
3a = 0 + -2

Combine like terms: 0 + -2 = -2
3a = -2

Divide each side by '3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Solution
a = {0, -2, -0.6666666667}