48a^4-22a^3b+2a^2b^2=0

Solution for 48a^4-22a^3b+2a^2b^2=0 equation:

Simplifying
48a4 + -22a3b + 2a2b2 = 0

Reorder the terms:
2a2b2 + -22a3b + 48a4 = 0

Solving
2a2b2 + -22a3b + 48a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(b2 + -11ab + 24a2) = 0

Factor a trinomial.
2a2((b + -8a)(b + -3a)) = 0

Ignore the factor 2.
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 '(b + -8a)' equal to zero and attempt to solve:

Simplifying
b + -8a = 0

Reorder the terms:
-8a + b = 0

Solving
-8a + b = 0

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

Add '-1b' to each side of the equation.
-8a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-8a + 0 = 0 + -1b
-8a = 0 + -1b
Remove the zero:
-8a = -1b

Divide each side by '-8'.
a = 0.125b

Simplifying
a = 0.125b
Subproblem 3
Set the factor '(b + -3a)' equal to zero and attempt to solve:

Simplifying
b + -3a = 0

Reorder the terms:
-3a + b = 0

Solving
-3a + b = 0

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

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

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

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

Simplifying
a = 0.3333333333b
Solution
a = {0, 0.125b, 0.3333333333b}