0=4x^4+4x^3+5x^2+4x+1

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Solution for 0=4x^4+4x^3+5x^2+4x+1 equation: 


Simplifying
0 = 4x4 + 4x3 + 5x2 + 4x + 1

Reorder the terms:
0 = 1 + 4x + 5x2 + 4x3 + 4x4

Solving
0 = 1 + 4x + 5x2 + 4x3 + 4x4

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -4x + -5x2 + -4x3 + -4x4 = 1 + 4x + 5x2 + 4x3 + 4x4 + -1 + -4x + -5x2 + -4x3 + -4x4

Reorder the terms:
-1 + -4x + -5x2 + -4x3 + -4x4 = 1 + -1 + 4x + -4x + 5x2 + -5x2 + 4x3 + -4x3 + 4x4 + -4x4

Combine like terms: 1 + -1 = 0
-1 + -4x + -5x2 + -4x3 + -4x4 = 0 + 4x + -4x + 5x2 + -5x2 + 4x3 + -4x3 + 4x4 + -4x4
-1 + -4x + -5x2 + -4x3 + -4x4 = 4x + -4x + 5x2 + -5x2 + 4x3 + -4x3 + 4x4 + -4x4

Combine like terms: 4x + -4x = 0
-1 + -4x + -5x2 + -4x3 + -4x4 = 0 + 5x2 + -5x2 + 4x3 + -4x3 + 4x4 + -4x4
-1 + -4x + -5x2 + -4x3 + -4x4 = 5x2 + -5x2 + 4x3 + -4x3 + 4x4 + -4x4

Combine like terms: 5x2 + -5x2 = 0
-1 + -4x + -5x2 + -4x3 + -4x4 = 0 + 4x3 + -4x3 + 4x4 + -4x4
-1 + -4x + -5x2 + -4x3 + -4x4 = 4x3 + -4x3 + 4x4 + -4x4

Combine like terms: 4x3 + -4x3 = 0
-1 + -4x + -5x2 + -4x3 + -4x4 = 0 + 4x4 + -4x4
-1 + -4x + -5x2 + -4x3 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
-1 + -4x + -5x2 + -4x3 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 4x + 5x2 + 4x3 + 4x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 4x + 5x2 + 4x3 + 4x4)' equal to zero and attempt to solve:

Simplifying
1 + 4x + 5x2 + 4x3 + 4x4 = 0

Solving
1 + 4x + 5x2 + 4x3 + 4x4 = 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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