F(a)=a^4+2a^3-4a^2-a

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Solution for F(a)=a^4+2a^3-4a^2-a equation: 


Simplifying
F(a) = a4 + 2a3 + -4a2 + -1a

Multiply F * a
aF = a4 + 2a3 + -4a2 + -1a

Reorder the terms:
aF = -1a + -4a2 + 2a3 + a4

Solving
aF = -1a + -4a2 + 2a3 + a4

Solving for variable 'a'.

Reorder the terms:
a + aF + 4a2 + -2a3 + -1a4 = -1a + -4a2 + 2a3 + a4 + a + 4a2 + -2a3 + -1a4

Reorder the terms:
a + aF + 4a2 + -2a3 + -1a4 = -1a + a + -4a2 + 4a2 + 2a3 + -2a3 + a4 + -1a4

Combine like terms: -1a + a = 0
a + aF + 4a2 + -2a3 + -1a4 = 0 + -4a2 + 4a2 + 2a3 + -2a3 + a4 + -1a4
a + aF + 4a2 + -2a3 + -1a4 = -4a2 + 4a2 + 2a3 + -2a3 + a4 + -1a4

Combine like terms: -4a2 + 4a2 = 0
a + aF + 4a2 + -2a3 + -1a4 = 0 + 2a3 + -2a3 + a4 + -1a4
a + aF + 4a2 + -2a3 + -1a4 = 2a3 + -2a3 + a4 + -1a4

Combine like terms: 2a3 + -2a3 = 0
a + aF + 4a2 + -2a3 + -1a4 = 0 + a4 + -1a4
a + aF + 4a2 + -2a3 + -1a4 = a4 + -1a4

Combine like terms: a4 + -1a4 = 0
a + aF + 4a2 + -2a3 + -1a4 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + F + 4a + -2a2 + -1a3) = 0


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(1 + F + 4a + -2a2 + -1a3)' equal to zero and attempt to solve:

Simplifying
1 + F + 4a + -2a2 + -1a3 = 0

Solving
1 + F + 4a + -2a2 + -1a3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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