48a^4b+4a^3b^2-4a^2b^3=

Solution for 48a^4b+4a^3b^2-4a^2b^3= equation:

Simplifying
48a4b + 4a3b2 + -4a2b3 = 0

Reorder the terms:
-4a2b3 + 4a3b2 + 48a4b = 0

Solving
-4a2b3 + 4a3b2 + 48a4b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a2b'.
4a2b(-1b2 + ab + 12a2) = 0

Factor a trinomial.
4a2b((-1b + -3a)(b + -4a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a2b' equal to zero and attempt to solve:

Simplifying
a2b = 0

Solving
a2b = 0

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

Simplifying
a2b = 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 '(-1b + -3a)' equal to zero and attempt to solve:

Simplifying
-1b + -3a = 0

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

Solving
-3a + -1b = 0

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

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

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

Divide each side by '-3'.
a = -0.3333333333b

Simplifying
a = -0.3333333333b
Subproblem 3
Set the factor '(b + -4a)' equal to zero and attempt to solve:

Simplifying
b + -4a = 0

Reorder the terms:
-4a + b = 0

Solving
-4a + b = 0

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

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

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

Divide each side by '-4'.
a = 0.25b

Simplifying
a = 0.25b
Solution
a = {-0.3333333333b, 0.25b}