(x-2)(x-3)(x-4)(x-6)=144

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Solution for (x-2)(x-3)(x-4)(x-6)=144 equation:


Simplifying
(x + -2)(x + -3)(x + -4)(x + -6) = 144

Reorder the terms:
(-2 + x)(x + -3)(x + -4)(x + -6) = 144

Reorder the terms:
(-2 + x)(-3 + x)(x + -4)(x + -6) = 144

Reorder the terms:
(-2 + x)(-3 + x)(-4 + x)(x + -6) = 144

Reorder the terms:
(-2 + x)(-3 + x)(-4 + x)(-6 + x) = 144

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x))(-4 + x)(-6 + x) = 144
((-3 * -2 + x * -2) + x(-3 + x))(-4 + x)(-6 + x) = 144
((6 + -2x) + x(-3 + x))(-4 + x)(-6 + x) = 144
(6 + -2x + (-3 * x + x * x))(-4 + x)(-6 + x) = 144
(6 + -2x + (-3x + x2))(-4 + x)(-6 + x) = 144

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2)(-4 + x)(-6 + x) = 144

Multiply (6 + -5x + x2) * (-4 + x)
(6(-4 + x) + -5x * (-4 + x) + x2(-4 + x))(-6 + x) = 144
((-4 * 6 + x * 6) + -5x * (-4 + x) + x2(-4 + x))(-6 + x) = 144
((-24 + 6x) + -5x * (-4 + x) + x2(-4 + x))(-6 + x) = 144
(-24 + 6x + (-4 * -5x + x * -5x) + x2(-4 + x))(-6 + x) = 144
(-24 + 6x + (20x + -5x2) + x2(-4 + x))(-6 + x) = 144
(-24 + 6x + 20x + -5x2 + (-4 * x2 + x * x2))(-6 + x) = 144
(-24 + 6x + 20x + -5x2 + (-4x2 + x3))(-6 + x) = 144

Combine like terms: 6x + 20x = 26x
(-24 + 26x + -5x2 + -4x2 + x3)(-6 + x) = 144

Combine like terms: -5x2 + -4x2 = -9x2
(-24 + 26x + -9x2 + x3)(-6 + x) = 144

Multiply (-24 + 26x + -9x2 + x3) * (-6 + x)
(-24(-6 + x) + 26x * (-6 + x) + -9x2 * (-6 + x) + x3(-6 + x)) = 144
((-6 * -24 + x * -24) + 26x * (-6 + x) + -9x2 * (-6 + x) + x3(-6 + x)) = 144
((144 + -24x) + 26x * (-6 + x) + -9x2 * (-6 + x) + x3(-6 + x)) = 144
(144 + -24x + (-6 * 26x + x * 26x) + -9x2 * (-6 + x) + x3(-6 + x)) = 144
(144 + -24x + (-156x + 26x2) + -9x2 * (-6 + x) + x3(-6 + x)) = 144
(144 + -24x + -156x + 26x2 + (-6 * -9x2 + x * -9x2) + x3(-6 + x)) = 144
(144 + -24x + -156x + 26x2 + (54x2 + -9x3) + x3(-6 + x)) = 144
(144 + -24x + -156x + 26x2 + 54x2 + -9x3 + (-6 * x3 + x * x3)) = 144
(144 + -24x + -156x + 26x2 + 54x2 + -9x3 + (-6x3 + x4)) = 144

Combine like terms: -24x + -156x = -180x
(144 + -180x + 26x2 + 54x2 + -9x3 + -6x3 + x4) = 144

Combine like terms: 26x2 + 54x2 = 80x2
(144 + -180x + 80x2 + -9x3 + -6x3 + x4) = 144

Combine like terms: -9x3 + -6x3 = -15x3
(144 + -180x + 80x2 + -15x3 + x4) = 144

Add '-144' to each side of the equation.
144 + -180x + 80x2 + -15x3 + -144 + x4 = 144 + -144

Reorder the terms:
144 + -144 + -180x + 80x2 + -15x3 + x4 = 144 + -144

Combine like terms: 144 + -144 = 0
0 + -180x + 80x2 + -15x3 + x4 = 144 + -144
-180x + 80x2 + -15x3 + x4 = 144 + -144

Combine like terms: 144 + -144 = 0
-180x + 80x2 + -15x3 + x4 = 0

Solving
-180x + 80x2 + -15x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-180 + 80x + -15x2 + 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 '(-180 + 80x + -15x2 + x3)' equal to zero and attempt to solve: Simplifying -180 + 80x + -15x2 + x3 = 0 Solving -180 + 80x + -15x2 + 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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