(2x+1)(x^2-2x+1)+(x+5)(4x^2+4x+1)=0

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Solution for (2x+1)(x^2-2x+1)+(x+5)(4x^2+4x+1)=0 equation: 


Simplifying
(2x + 1)(x2 + -2x + 1) + (x + 5)(4x2 + 4x + 1) = 0

Reorder the terms:
(1 + 2x)(x2 + -2x + 1) + (x + 5)(4x2 + 4x + 1) = 0

Reorder the terms:
(1 + 2x)(1 + -2x + x2) + (x + 5)(4x2 + 4x + 1) = 0

Multiply (1 + 2x) * (1 + -2x + x2)
(1(1 + -2x + x2) + 2x * (1 + -2x + x2)) + (x + 5)(4x2 + 4x + 1) = 0
((1 * 1 + -2x * 1 + x2 * 1) + 2x * (1 + -2x + x2)) + (x + 5)(4x2 + 4x + 1) = 0
((1 + -2x + 1x2) + 2x * (1 + -2x + x2)) + (x + 5)(4x2 + 4x + 1) = 0
(1 + -2x + 1x2 + (1 * 2x + -2x * 2x + x2 * 2x)) + (x + 5)(4x2 + 4x + 1) = 0
(1 + -2x + 1x2 + (2x + -4x2 + 2x3)) + (x + 5)(4x2 + 4x + 1) = 0

Reorder the terms:
(1 + -2x + 2x + 1x2 + -4x2 + 2x3) + (x + 5)(4x2 + 4x + 1) = 0

Combine like terms: -2x + 2x = 0
(1 + 0 + 1x2 + -4x2 + 2x3) + (x + 5)(4x2 + 4x + 1) = 0
(1 + 1x2 + -4x2 + 2x3) + (x + 5)(4x2 + 4x + 1) = 0

Combine like terms: 1x2 + -4x2 = -3x2
(1 + -3x2 + 2x3) + (x + 5)(4x2 + 4x + 1) = 0

Reorder the terms:
1 + -3x2 + 2x3 + (5 + x)(4x2 + 4x + 1) = 0

Reorder the terms:
1 + -3x2 + 2x3 + (5 + x)(1 + 4x + 4x2) = 0

Multiply (5 + x) * (1 + 4x + 4x2)
1 + -3x2 + 2x3 + (5(1 + 4x + 4x2) + x(1 + 4x + 4x2)) = 0
1 + -3x2 + 2x3 + ((1 * 5 + 4x * 5 + 4x2 * 5) + x(1 + 4x + 4x2)) = 0
1 + -3x2 + 2x3 + ((5 + 20x + 20x2) + x(1 + 4x + 4x2)) = 0
1 + -3x2 + 2x3 + (5 + 20x + 20x2 + (1 * x + 4x * x + 4x2 * x)) = 0
1 + -3x2 + 2x3 + (5 + 20x + 20x2 + (1x + 4x2 + 4x3)) = 0

Reorder the terms:
1 + -3x2 + 2x3 + (5 + 20x + 1x + 20x2 + 4x2 + 4x3) = 0

Combine like terms: 20x + 1x = 21x
1 + -3x2 + 2x3 + (5 + 21x + 20x2 + 4x2 + 4x3) = 0

Combine like terms: 20x2 + 4x2 = 24x2
1 + -3x2 + 2x3 + (5 + 21x + 24x2 + 4x3) = 0

Reorder the terms:
1 + 5 + 21x + -3x2 + 24x2 + 2x3 + 4x3 = 0

Combine like terms: 1 + 5 = 6
6 + 21x + -3x2 + 24x2 + 2x3 + 4x3 = 0

Combine like terms: -3x2 + 24x2 = 21x2
6 + 21x + 21x2 + 2x3 + 4x3 = 0

Combine like terms: 2x3 + 4x3 = 6x3
6 + 21x + 21x2 + 6x3 = 0

Solving
6 + 21x + 21x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 7x + 7x2 + 2x3) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + 7x + 7x2 + 2x3)' equal to zero and attempt to solve:

Simplifying
2 + 7x + 7x2 + 2x3 = 0

Solving
2 + 7x + 7x2 + 2x3 = 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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