(x-4)(x-3)(x-2)(x-1)=24

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Solution for (x-4)(x-3)(x-2)(x-1)=24 equation:


Simplifying
(x + -4)(x + -3)(x + -2)(x + -1) = 24

Reorder the terms:
(-4 + x)(x + -3)(x + -2)(x + -1) = 24

Reorder the terms:
(-4 + x)(-3 + x)(x + -2)(x + -1) = 24

Reorder the terms:
(-4 + x)(-3 + x)(-2 + x)(x + -1) = 24

Reorder the terms:
(-4 + x)(-3 + x)(-2 + x)(-1 + x) = 24

Multiply (-4 + x) * (-3 + x)
(-4(-3 + x) + x(-3 + x))(-2 + x)(-1 + x) = 24
((-3 * -4 + x * -4) + x(-3 + x))(-2 + x)(-1 + x) = 24
((12 + -4x) + x(-3 + x))(-2 + x)(-1 + x) = 24
(12 + -4x + (-3 * x + x * x))(-2 + x)(-1 + x) = 24
(12 + -4x + (-3x + x2))(-2 + x)(-1 + x) = 24

Combine like terms: -4x + -3x = -7x
(12 + -7x + x2)(-2 + x)(-1 + x) = 24

Multiply (12 + -7x + x2) * (-2 + x)
(12(-2 + x) + -7x * (-2 + x) + x2(-2 + x))(-1 + x) = 24
((-2 * 12 + x * 12) + -7x * (-2 + x) + x2(-2 + x))(-1 + x) = 24
((-24 + 12x) + -7x * (-2 + x) + x2(-2 + x))(-1 + x) = 24
(-24 + 12x + (-2 * -7x + x * -7x) + x2(-2 + x))(-1 + x) = 24
(-24 + 12x + (14x + -7x2) + x2(-2 + x))(-1 + x) = 24
(-24 + 12x + 14x + -7x2 + (-2 * x2 + x * x2))(-1 + x) = 24
(-24 + 12x + 14x + -7x2 + (-2x2 + x3))(-1 + x) = 24

Combine like terms: 12x + 14x = 26x
(-24 + 26x + -7x2 + -2x2 + x3)(-1 + x) = 24

Combine like terms: -7x2 + -2x2 = -9x2
(-24 + 26x + -9x2 + x3)(-1 + x) = 24

Multiply (-24 + 26x + -9x2 + x3) * (-1 + x)
(-24(-1 + x) + 26x * (-1 + x) + -9x2 * (-1 + x) + x3(-1 + x)) = 24
((-1 * -24 + x * -24) + 26x * (-1 + x) + -9x2 * (-1 + x) + x3(-1 + x)) = 24
((24 + -24x) + 26x * (-1 + x) + -9x2 * (-1 + x) + x3(-1 + x)) = 24
(24 + -24x + (-1 * 26x + x * 26x) + -9x2 * (-1 + x) + x3(-1 + x)) = 24
(24 + -24x + (-26x + 26x2) + -9x2 * (-1 + x) + x3(-1 + x)) = 24
(24 + -24x + -26x + 26x2 + (-1 * -9x2 + x * -9x2) + x3(-1 + x)) = 24
(24 + -24x + -26x + 26x2 + (9x2 + -9x3) + x3(-1 + x)) = 24
(24 + -24x + -26x + 26x2 + 9x2 + -9x3 + (-1 * x3 + x * x3)) = 24
(24 + -24x + -26x + 26x2 + 9x2 + -9x3 + (-1x3 + x4)) = 24

Combine like terms: -24x + -26x = -50x
(24 + -50x + 26x2 + 9x2 + -9x3 + -1x3 + x4) = 24

Combine like terms: 26x2 + 9x2 = 35x2
(24 + -50x + 35x2 + -9x3 + -1x3 + x4) = 24

Combine like terms: -9x3 + -1x3 = -10x3
(24 + -50x + 35x2 + -10x3 + x4) = 24

Add '-24' to each side of the equation.
24 + -50x + 35x2 + -10x3 + -24 + x4 = 24 + -24

Reorder the terms:
24 + -24 + -50x + 35x2 + -10x3 + x4 = 24 + -24

Combine like terms: 24 + -24 = 0
0 + -50x + 35x2 + -10x3 + x4 = 24 + -24
-50x + 35x2 + -10x3 + x4 = 24 + -24

Combine like terms: 24 + -24 = 0
-50x + 35x2 + -10x3 + x4 = 0

Solving
-50x + 35x2 + -10x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-50 + 35x + -10x2 + x3) = 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 '(-50 + 35x + -10x2 + x3)' equal to zero and attempt to solve: Simplifying -50 + 35x + -10x2 + x3 = 0 Solving -50 + 35x + -10x2 + x3 = 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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