=(s+1)(5s^2+2s+1)

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Solution for =(s+1)(5s^2+2s+1) equation: 


Simplifying
0 = (s + 1)(5s2 + 2s + 1)

Reorder the terms:
0 = (1 + s)(5s2 + 2s + 1)

Reorder the terms:
0 = (1 + s)(1 + 2s + 5s2)

Multiply (1 + s) * (1 + 2s + 5s2)
0 = (1(1 + 2s + 5s2) + s(1 + 2s + 5s2))
0 = ((1 * 1 + 2s * 1 + 5s2 * 1) + s(1 + 2s + 5s2))
0 = ((1 + 2s + 5s2) + s(1 + 2s + 5s2))
0 = (1 + 2s + 5s2 + (1 * s + 2s * s + 5s2 * s))
0 = (1 + 2s + 5s2 + (1s + 2s2 + 5s3))

Reorder the terms:
0 = (1 + 2s + 1s + 5s2 + 2s2 + 5s3)

Combine like terms: 2s + 1s = 3s
0 = (1 + 3s + 5s2 + 2s2 + 5s3)

Combine like terms: 5s2 + 2s2 = 7s2
0 = (1 + 3s + 7s2 + 5s3)

Solving
0 = 1 + 3s + 7s2 + 5s3

Solving for variable 's'.

Combine like terms: 0 + -1 = -1
-1 + -3s + -7s2 + -5s3 = 1 + 3s + 7s2 + 5s3 + -1 + -3s + -7s2 + -5s3

Reorder the terms:
-1 + -3s + -7s2 + -5s3 = 1 + -1 + 3s + -3s + 7s2 + -7s2 + 5s3 + -5s3

Combine like terms: 1 + -1 = 0
-1 + -3s + -7s2 + -5s3 = 0 + 3s + -3s + 7s2 + -7s2 + 5s3 + -5s3
-1 + -3s + -7s2 + -5s3 = 3s + -3s + 7s2 + -7s2 + 5s3 + -5s3

Combine like terms: 3s + -3s = 0
-1 + -3s + -7s2 + -5s3 = 0 + 7s2 + -7s2 + 5s3 + -5s3
-1 + -3s + -7s2 + -5s3 = 7s2 + -7s2 + 5s3 + -5s3

Combine like terms: 7s2 + -7s2 = 0
-1 + -3s + -7s2 + -5s3 = 0 + 5s3 + -5s3
-1 + -3s + -7s2 + -5s3 = 5s3 + -5s3

Combine like terms: 5s3 + -5s3 = 0
-1 + -3s + -7s2 + -5s3 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 3s + 7s2 + 5s3) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 3s + 7s2 + 5s3)' equal to zero and attempt to solve:

Simplifying
1 + 3s + 7s2 + 5s3 = 0

Solving
1 + 3s + 7s2 + 5s3 = 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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