2a^3b-10a^2b^2+12ab^3=0

Solution for 2a^3b-10a^2b^2+12ab^3=0 equation:

Simplifying
2a3b + -10a2b2 + 12ab3 = 0

Reorder the terms:
12ab3 + -10a2b2 + 2a3b = 0

Solving
12ab3 + -10a2b2 + 2a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2ab'.
2ab(6b2 + -5ab + a2) = 0

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

Ignore the factor 2.
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 '(2b + -1a)' equal to zero and attempt to solve:

Simplifying
2b + -1a = 0

Reorder the terms:
-1a + 2b = 0

Solving
-1a + 2b = 0

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

Add '-2b' to each side of the equation.
-1a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
-1a + 0 = 0 + -2b
-1a = 0 + -2b
Remove the zero:
-1a = -2b

Divide each side by '-1'.
a = 2b

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

Simplifying
3b + -1a = 0

Reorder the terms:
-1a + 3b = 0

Solving
-1a + 3b = 0

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

Add '-3b' to each side of the equation.
-1a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
-1a + 0 = 0 + -3b
-1a = 0 + -3b
Remove the zero:
-1a = -3b

Divide each side by '-1'.
a = 3b

Simplifying
a = 3b
Solution
a = {2b, 3b}