12a^3b+8a^2b^2-20ab^3=

Solution for 12a^3b+8a^2b^2-20ab^3= equation:

Simplifying
12a3b + 8a2b2 + -20ab3 = 0

Reorder the terms:
-20ab3 + 8a2b2 + 12a3b = 0

Solving
-20ab3 + 8a2b2 + 12a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4ab'.
4ab(-5b2 + 2ab + 3a2) = 0

Factor a trinomial.
4ab((-5b + -3a)(b + -1a)) = 0

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

Simplifying
-5b + -3a = 0

Reorder the terms:
-3a + -5b = 0

Solving
-3a + -5b = 0

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

Add '5b' to each side of the equation.
-3a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
-3a + 0 = 0 + 5b
-3a = 0 + 5b
Remove the zero:
-3a = 5b

Divide each side by '-3'.
a = -1.666666667b

Simplifying
a = -1.666666667b
Subproblem 3
Set the factor '(b + -1a)' equal to zero and attempt to solve:

Simplifying
b + -1a = 0

Reorder the terms:
-1a + b = 0

Solving
-1a + b = 0

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

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

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

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

Simplifying
a = b
Solution
a = {-1.666666667b, b}