8a^2b^4c-24ab^4c+48ab^2=0

Solution for 8a^2b^4c-24ab^4c+48ab^2=0 equation:

Simplifying
8a2b4c + -24ab4c + 48ab2 = 0

Reorder the terms:
48ab2 + -24ab4c + 8a2b4c = 0

Solving
48ab2 + -24ab4c + 8a2b4c = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8ab2'.
8ab2(6 + -3b2c + ab2c) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'ab2' equal to zero and attempt to solve:

Simplifying
ab2 = 0

Solving
ab2 = 0

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

Simplifying
ab2 = 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 '(6 + -3b2c + ab2c)' equal to zero and attempt to solve:

Simplifying
6 + -3b2c + ab2c = 0

Reorder the terms:
6 + ab2c + -3b2c = 0

Solving
6 + ab2c + -3b2c = 0

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

Add '-6' to each side of the equation.
6 + ab2c + -6 + -3b2c = 0 + -6

Reorder the terms:
6 + -6 + ab2c + -3b2c = 0 + -6

Combine like terms: 6 + -6 = 0
0 + ab2c + -3b2c = 0 + -6
ab2c + -3b2c = 0 + -6

Combine like terms: 0 + -6 = -6
ab2c + -3b2c = -6

Add '3b2c' to each side of the equation.
ab2c + -3b2c + 3b2c = -6 + 3b2c

Combine like terms: -3b2c + 3b2c = 0
ab2c + 0 = -6 + 3b2c
ab2c = -6 + 3b2c

Divide each side by 'b2c'.
a = -6b-2c-1 + 3

Simplifying
a = -6b-2c-1 + 3

Reorder the terms:
a = 3 + -6b-2c-1
Solution
a = {3 + -6b-2c-1}