P(x)=x^6+5x^5+7x^4+3x^3

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Solution for P(x)=x^6+5x^5+7x^4+3x^3 equation: 


Simplifying
P(x) = x6 + 5x5 + 7x4 + 3x3

Multiply P * x
xP = x6 + 5x5 + 7x4 + 3x3

Reorder the terms:
xP = 3x3 + 7x4 + 5x5 + x6

Solving
xP = 3x3 + 7x4 + 5x5 + x6

Solving for variable 'x'.

Reorder the terms:
xP + -3x3 + -7x4 + -5x5 + -1x6 = 3x3 + -3x3 + 7x4 + -7x4 + 5x5 + -5x5 + x6 + -1x6

Combine like terms: 3x3 + -3x3 = 0
xP + -3x3 + -7x4 + -5x5 + -1x6 = 0 + 7x4 + -7x4 + 5x5 + -5x5 + x6 + -1x6
xP + -3x3 + -7x4 + -5x5 + -1x6 = 7x4 + -7x4 + 5x5 + -5x5 + x6 + -1x6

Combine like terms: 7x4 + -7x4 = 0
xP + -3x3 + -7x4 + -5x5 + -1x6 = 0 + 5x5 + -5x5 + x6 + -1x6
xP + -3x3 + -7x4 + -5x5 + -1x6 = 5x5 + -5x5 + x6 + -1x6

Combine like terms: 5x5 + -5x5 = 0
xP + -3x3 + -7x4 + -5x5 + -1x6 = 0 + x6 + -1x6
xP + -3x3 + -7x4 + -5x5 + -1x6 = x6 + -1x6

Combine like terms: x6 + -1x6 = 0
xP + -3x3 + -7x4 + -5x5 + -1x6 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(P + -3x2 + -7x3 + -5x4 + -1x5) = 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 '(P + -3x2 + -7x3 + -5x4 + -1x5)' equal to zero and attempt to solve:

Simplifying
P + -3x2 + -7x3 + -5x4 + -1x5 = 0

Solving
P + -3x2 + -7x3 + -5x4 + -1x5 = 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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