12a^3+2a^2=0

Solution for 12a^3+2a^2=0 equation:

Simplifying
12a3 + 2a2 = 0

Reorder the terms:
2a2 + 12a3 = 0

Solving
2a2 + 12a3 = 0

Solving for variable 'a'.

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

Ignore the factor 2.
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 '(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, -0.1666666667}