x(x-1)(x-2)(x-3)(x-4)(x-5)=0

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Solution for x(x-1)(x-2)(x-3)(x-4)(x-5)=0 equation: 


Simplifying
x(x + -1)(x + -2)(x + -3)(x + -4)(x + -5) = 0

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

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

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

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

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

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

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

Multiply (2 + -3x + x2) * (-3 + x)
x(2(-3 + x) + -3x * (-3 + x) + x2(-3 + x))(-4 + x)(-5 + x) = 0
x((-3 * 2 + x * 2) + -3x * (-3 + x) + x2(-3 + x))(-4 + x)(-5 + x) = 0
x((-6 + 2x) + -3x * (-3 + x) + x2(-3 + x))(-4 + x)(-5 + x) = 0
x(-6 + 2x + (-3 * -3x + x * -3x) + x2(-3 + x))(-4 + x)(-5 + x) = 0
x(-6 + 2x + (9x + -3x2) + x2(-3 + x))(-4 + x)(-5 + x) = 0
x(-6 + 2x + 9x + -3x2 + (-3 * x2 + x * x2))(-4 + x)(-5 + x) = 0
x(-6 + 2x + 9x + -3x2 + (-3x2 + x3))(-4 + x)(-5 + x) = 0

Combine like terms: 2x + 9x = 11x
x(-6 + 11x + -3x2 + -3x2 + x3)(-4 + x)(-5 + x) = 0

Combine like terms: -3x2 + -3x2 = -6x2
x(-6 + 11x + -6x2 + x3)(-4 + x)(-5 + x) = 0

Multiply (-6 + 11x + -6x2 + x3) * (-4 + x)
x(-6(-4 + x) + 11x * (-4 + x) + -6x2 * (-4 + x) + x3(-4 + x))(-5 + x) = 0
x((-4 * -6 + x * -6) + 11x * (-4 + x) + -6x2 * (-4 + x) + x3(-4 + x))(-5 + x) = 0
x((24 + -6x) + 11x * (-4 + x) + -6x2 * (-4 + x) + x3(-4 + x))(-5 + x) = 0
x(24 + -6x + (-4 * 11x + x * 11x) + -6x2 * (-4 + x) + x3(-4 + x))(-5 + x) = 0
x(24 + -6x + (-44x + 11x2) + -6x2 * (-4 + x) + x3(-4 + x))(-5 + x) = 0
x(24 + -6x + -44x + 11x2 + (-4 * -6x2 + x * -6x2) + x3(-4 + x))(-5 + x) = 0
x(24 + -6x + -44x + 11x2 + (24x2 + -6x3) + x3(-4 + x))(-5 + x) = 0
x(24 + -6x + -44x + 11x2 + 24x2 + -6x3 + (-4 * x3 + x * x3))(-5 + x) = 0
x(24 + -6x + -44x + 11x2 + 24x2 + -6x3 + (-4x3 + x4))(-5 + x) = 0

Combine like terms: -6x + -44x = -50x
x(24 + -50x + 11x2 + 24x2 + -6x3 + -4x3 + x4)(-5 + x) = 0

Combine like terms: 11x2 + 24x2 = 35x2
x(24 + -50x + 35x2 + -6x3 + -4x3 + x4)(-5 + x) = 0

Combine like terms: -6x3 + -4x3 = -10x3
x(24 + -50x + 35x2 + -10x3 + x4)(-5 + x) = 0

Multiply (24 + -50x + 35x2 + -10x3 + x4) * (-5 + x)
x(24(-5 + x) + -50x * (-5 + x) + 35x2 * (-5 + x) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x((-5 * 24 + x * 24) + -50x * (-5 + x) + 35x2 * (-5 + x) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x((-120 + 24x) + -50x * (-5 + x) + 35x2 * (-5 + x) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x(-120 + 24x + (-5 * -50x + x * -50x) + 35x2 * (-5 + x) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x(-120 + 24x + (250x + -50x2) + 35x2 * (-5 + x) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x(-120 + 24x + 250x + -50x2 + (-5 * 35x2 + x * 35x2) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x(-120 + 24x + 250x + -50x2 + (-175x2 + 35x3) + -10x3 * (-5 + x) + x4(-5 + x)) = 0
x(-120 + 24x + 250x + -50x2 + -175x2 + 35x3 + (-5 * -10x3 + x * -10x3) + x4(-5 + x)) = 0
x(-120 + 24x + 250x + -50x2 + -175x2 + 35x3 + (50x3 + -10x4) + x4(-5 + x)) = 0
x(-120 + 24x + 250x + -50x2 + -175x2 + 35x3 + 50x3 + -10x4 + (-5 * x4 + x * x4)) = 0
x(-120 + 24x + 250x + -50x2 + -175x2 + 35x3 + 50x3 + -10x4 + (-5x4 + x5)) = 0

Combine like terms: 24x + 250x = 274x
x(-120 + 274x + -50x2 + -175x2 + 35x3 + 50x3 + -10x4 + -5x4 + x5) = 0

Combine like terms: -50x2 + -175x2 = -225x2
x(-120 + 274x + -225x2 + 35x3 + 50x3 + -10x4 + -5x4 + x5) = 0

Combine like terms: 35x3 + 50x3 = 85x3
x(-120 + 274x + -225x2 + 85x3 + -10x4 + -5x4 + x5) = 0

Combine like terms: -10x4 + -5x4 = -15x4
x(-120 + 274x + -225x2 + 85x3 + -15x4 + x5) = 0
(-120 * x + 274x * x + -225x2 * x + 85x3 * x + -15x4 * x + x5 * x) = 0
(-120x + 274x2 + -225x3 + 85x4 + -15x5 + x6) = 0

Solving
-120x + 274x2 + -225x3 + 85x4 + -15x5 + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-120 + 274x + -225x2 + 85x3 + -15x4 + x5) = 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 '(-120 + 274x + -225x2 + 85x3 + -15x4 + x5)' equal to zero and attempt to solve:

Simplifying
-120 + 274x + -225x2 + 85x3 + -15x4 + x5 = 0

Solving
-120 + 274x + -225x2 + 85x3 + -15x4 + x5 = 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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