x^2-5x+1=x^4-10x^3+23x^2+10x+1

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Solution for x^2-5x+1=x^4-10x^3+23x^2+10x+1 equation: 


Simplifying
x2 + -5x + 1 = x4 + -10x3 + 23x2 + 10x + 1

Reorder the terms:
1 + -5x + x2 = x4 + -10x3 + 23x2 + 10x + 1

Reorder the terms:
1 + -5x + x2 = 1 + 10x + 23x2 + -10x3 + x4

Add '-1' to each side of the equation.
1 + -5x + -1 + x2 = 1 + 10x + 23x2 + -10x3 + -1 + x4

Reorder the terms:
1 + -1 + -5x + x2 = 1 + 10x + 23x2 + -10x3 + -1 + x4

Combine like terms: 1 + -1 = 0
0 + -5x + x2 = 1 + 10x + 23x2 + -10x3 + -1 + x4
-5x + x2 = 1 + 10x + 23x2 + -10x3 + -1 + x4

Reorder the terms:
-5x + x2 = 1 + -1 + 10x + 23x2 + -10x3 + x4

Combine like terms: 1 + -1 = 0
-5x + x2 = 0 + 10x + 23x2 + -10x3 + x4
-5x + x2 = 10x + 23x2 + -10x3 + x4

Solving
-5x + x2 = 10x + 23x2 + -10x3 + x4

Solving for variable 'x'.

Reorder the terms:
-5x + -10x + x2 + -23x2 + 10x3 + -1x4 = 10x + 23x2 + -10x3 + x4 + -10x + -23x2 + 10x3 + -1x4

Combine like terms: -5x + -10x = -15x
-15x + x2 + -23x2 + 10x3 + -1x4 = 10x + 23x2 + -10x3 + x4 + -10x + -23x2 + 10x3 + -1x4

Combine like terms: x2 + -23x2 = -22x2
-15x + -22x2 + 10x3 + -1x4 = 10x + 23x2 + -10x3 + x4 + -10x + -23x2 + 10x3 + -1x4

Reorder the terms:
-15x + -22x2 + 10x3 + -1x4 = 10x + -10x + 23x2 + -23x2 + -10x3 + 10x3 + x4 + -1x4

Combine like terms: 10x + -10x = 0
-15x + -22x2 + 10x3 + -1x4 = 0 + 23x2 + -23x2 + -10x3 + 10x3 + x4 + -1x4
-15x + -22x2 + 10x3 + -1x4 = 23x2 + -23x2 + -10x3 + 10x3 + x4 + -1x4

Combine like terms: 23x2 + -23x2 = 0
-15x + -22x2 + 10x3 + -1x4 = 0 + -10x3 + 10x3 + x4 + -1x4
-15x + -22x2 + 10x3 + -1x4 = -10x3 + 10x3 + x4 + -1x4

Combine like terms: -10x3 + 10x3 = 0
-15x + -22x2 + 10x3 + -1x4 = 0 + x4 + -1x4
-15x + -22x2 + 10x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-15x + -22x2 + 10x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + -22x + 10x2 + -1x3) = 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 '(-15 + -22x + 10x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-15 + -22x + 10x2 + -1x3 = 0

Solving
-15 + -22x + 10x2 + -1x3 = 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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