a^4+2a^3b-3a^2b^2=0

Solution for a^4+2a^3b-3a^2b^2=0 equation:

Simplifying
a4 + 2a3b + -3a2b2 = 0

Reorder the terms:
-3a2b2 + 2a3b + a4 = 0

Solving
-3a2b2 + 2a3b + a4 = 0

Solving for variable 'a'.

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

Factor a trinomial.
a2((-3b + -1a)(b + -1a)) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
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
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 = {0, -3b, b}