(12a^3)+(15a^2)=0

Solution for (12a^3)+(15a^2)=0 equation:

Simplifying
(12a3) + (15a2) = 0

Reorder the terms:
(15a2) + (12a3) = 0

Solving
(15a2) + (12a3) = 0

Solving for variable 'a'.

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

Ignore the factor 3.
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 '(5 + (4a))' equal to zero and attempt to solve:

Simplifying
5 + (4a) = 0

Solving
5 + (4a) = 0

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

Add '-5' to each side of the equation.
5 + -5 + (4a) = 0 + -5

Combine like terms: 5 + -5 = 0
0 + (4a) = 0 + -5
(4a) = 0 + -5

Combine like terms: 0 + -5 = -5
(4a) = -5

Divide each side by '4'.
a = -1.25

Simplifying
a = -1.25
Solution
a = {0, -1.25}