3a(6a+1)(2a+1)=0

Solution for 3a(6a+1)(2a+1)=0 equation:

Simplifying
3a(6a + 1)(2a + 1) = 0

Reorder the terms:
3a(1 + 6a)(2a + 1) = 0

Reorder the terms:
3a(1 + 6a)(1 + 2a) = 0

Multiply (1 + 6a) * (1 + 2a)
3a(1(1 + 2a) + 6a * (1 + 2a)) = 0
3a((1 * 1 + 2a * 1) + 6a * (1 + 2a)) = 0
3a((1 + 2a) + 6a * (1 + 2a)) = 0
3a(1 + 2a + (1 * 6a + 2a * 6a)) = 0
3a(1 + 2a + (6a + 12a2)) = 0

Combine like terms: 2a + 6a = 8a
3a(1 + 8a + 12a2) = 0
(1 * 3a + 8a * 3a + 12a2 * 3a) = 0
(3a + 24a2 + 36a3) = 0

Solving
3a + 24a2 + 36a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(1 + 8a + 12a2) = 0

Factor a trinomial.
3a((1 + 2a)(1 + 6a)) = 0

Ignore the factor 3.
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 '(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
Subproblem 3
Set the factor '(1 + 6a)' equal to zero and attempt to solve:

Simplifying
1 + 6a = 0

Solving
1 + 6a = 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 + 6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6a = 0 + -1
6a = 0 + -1

Combine like terms: 0 + -1 = -1
6a = -1

Divide each side by '6'.
a = -0.1666666667

Simplifying
a = -0.1666666667
Solution
a = {0, -0.5, -0.1666666667}