36a^8b^3c+16a^3b^5c^4-8a^7b=8a^3b(4a^5b^2c+2b^2c^4-a^2)

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Solution for 36a^8b^3c+16a^3b^5c^4-8a^7b=8a^3b(4a^5b^2c+2b^2c^4-a^2) equation: 


Simplifying
36a8b3c + 16a3b5c4 + -8a7b = 8a3b(4a5b2c + 2b2c4 + -1a2)

Reorder the terms:
16a3b5c4 + -8a7b + 36a8b3c = 8a3b(4a5b2c + 2b2c4 + -1a2)

Reorder the terms:
16a3b5c4 + -8a7b + 36a8b3c = 8a3b(-1a2 + 4a5b2c + 2b2c4)
16a3b5c4 + -8a7b + 36a8b3c = (-1a2 * 8a3b + 4a5b2c * 8a3b + 2b2c4 * 8a3b)

Reorder the terms:
16a3b5c4 + -8a7b + 36a8b3c = (16a3b3c4 + -8a5b + 32a8b3c)
16a3b5c4 + -8a7b + 36a8b3c = (16a3b3c4 + -8a5b + 32a8b3c)

Solving
16a3b5c4 + -8a7b + 36a8b3c = 16a3b3c4 + -8a5b + 32a8b3c

Solving for variable 'a'.

Reorder the terms:
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 36a8b3c + -32a8b3c = 16a3b3c4 + -8a5b + 32a8b3c + -16a3b3c4 + 8a5b + -32a8b3c

Combine like terms: 36a8b3c + -32a8b3c = 4a8b3c
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = 16a3b3c4 + -8a5b + 32a8b3c + -16a3b3c4 + 8a5b + -32a8b3c

Reorder the terms:
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = 16a3b3c4 + -16a3b3c4 + -8a5b + 8a5b + 32a8b3c + -32a8b3c

Combine like terms: 16a3b3c4 + -16a3b3c4 = 0
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = 0 + -8a5b + 8a5b + 32a8b3c + -32a8b3c
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = -8a5b + 8a5b + 32a8b3c + -32a8b3c

Combine like terms: -8a5b + 8a5b = 0
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = 0 + 32a8b3c + -32a8b3c
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = 32a8b3c + -32a8b3c

Combine like terms: 32a8b3c + -32a8b3c = 0
-16a3b3c4 + 16a3b5c4 + 8a5b + -8a7b + 4a8b3c = 0

Factor out the Greatest Common Factor (GCF), '4a3b'.
4a3b(-4b2c4 + 4b4c4 + 2a2 + -2a4 + a5b2c) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'a3b' equal to zero and attempt to solve:

Simplifying
a3b = 0

Solving
a3b = 0

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

Simplifying
a3b = 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 '(-4b2c4 + 4b4c4 + 2a2 + -2a4 + a5b2c)' equal to zero and attempt to solve:

Simplifying
-4b2c4 + 4b4c4 + 2a2 + -2a4 + a5b2c = 0

Reorder the terms:
2a2 + -2a4 + a5b2c + -4b2c4 + 4b4c4 = 0

Solving
2a2 + -2a4 + a5b2c + -4b2c4 + 4b4c4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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