16a^2-a^6c^4=

Solution for 16a^2-a^6c^4= equation:

Simplifying
16a2 + -1a6c4 = 0

Solving
16a2 + -1a6c4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(16 + -1a4c4) = 0

Factor a difference between two squares.
a2((4 + a2c2)(4 + -1a2c2)) = 0

Factor a difference between two squares.
a2((4 + a2c2)((2 + ac)(2 + -1ac))) = 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 '(4 + a2c2)' equal to zero and attempt to solve:

Simplifying
4 + a2c2 = 0

Solving
4 + a2c2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + a2c2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a2c2 = 0 + -4
a2c2 = 0 + -4

Combine like terms: 0 + -4 = -4
a2c2 = -4

Divide each side by 'c2'.
a2 = -4c-2

Simplifying
a2 = -4c-2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + ac)' equal to zero and attempt to solve:

Simplifying
2 + ac = 0

Solving
2 + ac = 0

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

Add '-2' to each side of the equation.
2 + -2 + ac = 0 + -2

Combine like terms: 2 + -2 = 0
0 + ac = 0 + -2
ac = 0 + -2

Combine like terms: 0 + -2 = -2
ac = -2

Divide each side by 'c'.
a = -2c-1

Simplifying
a = -2c-1
Subproblem 4
Set the factor '(2 + -1ac)' equal to zero and attempt to solve:

Simplifying
2 + -1ac = 0

Solving
2 + -1ac = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1ac = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1ac = 0 + -2
-1ac = 0 + -2

Combine like terms: 0 + -2 = -2
-1ac = -2

Divide each side by '-1c'.
a = 2c-1

Simplifying
a = 2c-1
Solution
a = {0, -2c-1, 2c-1}