16a^3bc-49ab^3c=0

Solution for 16a^3bc-49ab^3c=0 equation:

Simplifying
16a3bc + -49ab3c = 0

Reorder the terms:
-49ab3c + 16a3bc = 0

Solving
-49ab3c + 16a3bc = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'abc'.
abc(-49b2 + 16a2) = 0

Factor a difference between two squares.
abc((7b + 4a)(-7b + 4a)) = 0

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

Simplifying
abc = 0

Solving
abc = 0

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

Simplifying
abc = 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 '(7b + 4a)' equal to zero and attempt to solve:

Simplifying
7b + 4a = 0

Reorder the terms:
4a + 7b = 0

Solving
4a + 7b = 0

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

Add '-7b' to each side of the equation.
4a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
4a + 0 = 0 + -7b
4a = 0 + -7b
Remove the zero:
4a = -7b

Divide each side by '4'.
a = -1.75b

Simplifying
a = -1.75b
Subproblem 3
Set the factor '(-7b + 4a)' equal to zero and attempt to solve:

Simplifying
-7b + 4a = 0

Reorder the terms:
4a + -7b = 0

Solving
4a + -7b = 0

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

Add '7b' to each side of the equation.
4a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
4a + 0 = 0 + 7b
4a = 0 + 7b
Remove the zero:
4a = 7b

Divide each side by '4'.
a = 1.75b

Simplifying
a = 1.75b
Solution
a = {-1.75b, 1.75b}