6ab+9a^2b-15a^3b=0

Solution for 6ab+9a^2b-15a^3b=0 equation:

Simplifying
6ab + 9a2b + -15a3b = 0

Solving
6ab + 9a2b + -15a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3ab'.
3ab(2 + 3a + -5a2) = 0

Factor a trinomial.
3ab((1 + -1a)(2 + 5a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve:

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Subproblem 3
Set the factor '(2 + 5a)' equal to zero and attempt to solve:

Simplifying
2 + 5a = 0

Solving
2 + 5a = 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 + 5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5a = 0 + -2
5a = 0 + -2

Combine like terms: 0 + -2 = -2
5a = -2

Divide each side by '5'.
a = -0.4

Simplifying
a = -0.4
Solution
a = {1, -0.4}