3a^3b-14a^2b^2+8ab^3=0

Solution for 3a^3b-14a^2b^2+8ab^3=0 equation:

Simplifying
3a3b + -14a2b2 + 8ab3 = 0

Reorder the terms:
8ab3 + -14a2b2 + 3a3b = 0

Solving
8ab3 + -14a2b2 + 3a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(8b2 + -14ab + 3a2) = 0

Factor a trinomial.
ab((2b + -3a)(4b + -1a)) = 0

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 + -3a)' equal to zero and attempt to solve:

Simplifying
2b + -3a = 0

Reorder the terms:
-3a + 2b = 0

Solving
-3a + 2b = 0

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

Add '-2b' to each side of the equation.
-3a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
-3a + 0 = 0 + -2b
-3a = 0 + -2b
Remove the zero:
-3a = -2b

Divide each side by '-3'.
a = 0.6666666667b

Simplifying
a = 0.6666666667b
Subproblem 3
Set the factor '(4b + -1a)' equal to zero and attempt to solve:

Simplifying
4b + -1a = 0

Reorder the terms:
-1a + 4b = 0

Solving
-1a + 4b = 0

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

Add '-4b' to each side of the equation.
-1a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
-1a + 0 = 0 + -4b
-1a = 0 + -4b
Remove the zero:
-1a = -4b

Divide each side by '-1'.
a = 4b

Simplifying
a = 4b
Solution
a = {0.6666666667b, 4b}