0=x^5-10x^4+27x^3-2x^2-40x

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Solution for 0=x^5-10x^4+27x^3-2x^2-40x equation: 


Simplifying
0 = x5 + -10x4 + 27x3 + -2x2 + -40x

Reorder the terms:
0 = -40x + -2x2 + 27x3 + -10x4 + x5

Solving
0 = -40x + -2x2 + 27x3 + -10x4 + x5

Solving for variable 'x'.
Remove the zero:
40x + 2x2 + -27x3 + 10x4 + -1x5 = -40x + -2x2 + 27x3 + -10x4 + x5 + 40x + 2x2 + -27x3 + 10x4 + -1x5

Reorder the terms:
40x + 2x2 + -27x3 + 10x4 + -1x5 = -40x + 40x + -2x2 + 2x2 + 27x3 + -27x3 + -10x4 + 10x4 + x5 + -1x5

Combine like terms: -40x + 40x = 0
40x + 2x2 + -27x3 + 10x4 + -1x5 = 0 + -2x2 + 2x2 + 27x3 + -27x3 + -10x4 + 10x4 + x5 + -1x5
40x + 2x2 + -27x3 + 10x4 + -1x5 = -2x2 + 2x2 + 27x3 + -27x3 + -10x4 + 10x4 + x5 + -1x5

Combine like terms: -2x2 + 2x2 = 0
40x + 2x2 + -27x3 + 10x4 + -1x5 = 0 + 27x3 + -27x3 + -10x4 + 10x4 + x5 + -1x5
40x + 2x2 + -27x3 + 10x4 + -1x5 = 27x3 + -27x3 + -10x4 + 10x4 + x5 + -1x5

Combine like terms: 27x3 + -27x3 = 0
40x + 2x2 + -27x3 + 10x4 + -1x5 = 0 + -10x4 + 10x4 + x5 + -1x5
40x + 2x2 + -27x3 + 10x4 + -1x5 = -10x4 + 10x4 + x5 + -1x5

Combine like terms: -10x4 + 10x4 = 0
40x + 2x2 + -27x3 + 10x4 + -1x5 = 0 + x5 + -1x5
40x + 2x2 + -27x3 + 10x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
40x + 2x2 + -27x3 + 10x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(40 + 2x + -27x2 + 10x3 + -1x4) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(40 + 2x + -27x2 + 10x3 + -1x4)' equal to zero and attempt to solve:

Simplifying
40 + 2x + -27x2 + 10x3 + -1x4 = 0

Solving
40 + 2x + -27x2 + 10x3 + -1x4 = 0

The solution to this equation could not be determined.

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

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